I'm having the same problem with a fresh install of MATE 20.04. After monitoring problem for a couple of days, I noticed that my syslog was less than 1MB in size for most of the day. I went out for a while. My computer went to screensaver. When I woke it up from screensaver and later checked the syslog, it was almost 1.5 GB in size. Here's the last hundred or so lines of my syslog:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 9 to 4 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 0 to 4 (1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 1 to 4 (-1) Prio: 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 7 from 8 to 4 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 1 to 4 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 1 to 4 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 8 to 4 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 1 to 4 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 8 to 4 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 1 to 4 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 2 to 4 (-1) Prio: 29
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 2 to 4 (-1) Prio: 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 2 to 4 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 2 to 4 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 8 to 2 (-1) Prio: 116
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 2 to 4 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 2 to 4 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 2 to 4 (1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 3 to 1 (-1) Prio: 64
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 6 to 4 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 6 to 4 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 8 to 4 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 7 to 4 (1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 8 to 4 (-1) Prio: 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 8 to 4 (-1) Prio: 39
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 8 to 4 (-1) Prio: 29
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 8 to 4 (-1) Prio: 34
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: print-layout-begin
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play0: |4S |3S |6S |5S |2S AS KS QS JS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play1: 5S 4S 3S 2S AS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play2: 8S 7S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play3:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play4:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play5:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play6: |9S |JS TS 9S 8S 7S 6S 5S 4S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play7: AS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play8: |3S |3S |QS |6S KS QS JS TS 9S 8S 7S KS 5S 4S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play9: 8S 7S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal0:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal1:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal2:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal3:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal4: |QS |JS |AS |9S |2S |6S |KS |TS |2S |TS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Off: KS KS KS KS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: print-layout-end
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: moves 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 0 to 3 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 0 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 0 to 3 (-1) Prio: -1
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 1 to 3 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 1 to 3 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 1 to 3 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 1 to 6 (-1) Prio: -33
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 1 to 8 (-1) Prio: -33
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 1 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 2 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 6 to 3 (-1) Prio: 29
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 6 to 3 (-1) Prio: 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 6 to 2 (-1) Prio: -23
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 6 to 3 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 6 to 9 (-1) Prio: -23
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 6 to 3 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 6 to 3 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 6 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 6 to 0 (1) Prio: -38
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 6 to 3 (1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 8 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 8 to 3 (-1) Prio: -1
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 9 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 14 to 0 (-1) Prio: 0
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: print-layout-begin
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play0: |4S |3S |6S |5S |2S AS KS QS JS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play1: 2S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play2: |8S KS 5S 4S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play3:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play4:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play5:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play6: |9S |JS TS KS QS JS TS 9S 8S 7S 6S 5S 4S 3S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play7: |AS |AS 7S QS JS TS 9S 8S 7S
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play8: |3S |3S |QS |6S KS QS JS TS 9S 8S 7S KS 5S 4S 9S 8S 7S 6S 5S 4S 3S 2S AS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Play9: 8S 7S 6S 5S 4S 3S 2S AS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal0:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal1:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal2:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal3:
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Deal4: |QS |JS |AS |9S |2S |6S |KS |TS |2S |TS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: Off: KS KS
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: print-layout-end
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: moves 37
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 0 to 3 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 0 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 9 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 1 to 6 (-1) Prio: 104
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 2 to 3 (-1) Prio: 4
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 9 to 3 (-1) Prio: 9
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 6 to 2 (-1) Prio: 7
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 0 from 6 to 3 (-1) Prio: 49
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 1 from 6 to 3 (-1) Prio: 44
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 2 from 6 to 3 (-1) Prio: 39
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 6 to 3 (-1) Prio: 34
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 9 to 3 (-1) Prio: 14
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 4 from 6 to 3 (-1) Prio: 29
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 5 from 6 to 3 (-1) Prio: 24
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 6 from 6 to 3 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 3 from 9 to 3 (-1) Prio: 19
May 17 17:03:34 jim-pc org.mate.panel.applet.BriskMenuFactory[14549]: move 7 from 6 to 3 (-1) Prio: 14