OK, got my widow decoration and controls back, so I can debug some.
UM 18.04 included the file /etc/compizconfig/mate.ini in compiz-mate, but that file is missing from compiz-mate in 20.04.
I presume that file was in compiz-mate in UM 19.10, but I don't have a copy of 19.10 to confirm. Can anyone with 19.10 see if the file was part of compiz-mate?
Without this file it is impossible to select "mate" in CCSM > Preferences > Profile, which was the default, already present, setting in 18.04. (It includes amoung other things the MATE logos for the cube, but also more important things like crash handlers, reverting to Marco, etc.)
Note there must be other files also missing because copying it over to 20.04 manually after the fact doesn't help.