At first I have tried the previous version from ppa:kranich/remastersys (1.8.402~ubuntu16.10.1 which really built by ~nemh) on Ubuntu MATE 18.04 LTS. It has some problems with D-Bus too.
$ cat .xsession-errors | grep -i error | grep -i dbus
(process:1944): indicator-sound-WARNING **: 00:11:53.772: accounts-service-access.vala:218: unable to sync volume 0,446686 to AccountsService: GDBus.Error:org.freedesktop.DBus.Error.InvalidArgs: No such interface 'com.ubuntu.AccountsService.Sound'
$ sudo grep -ir error /var/log/ | grep -i dbus
/var/log/syslog:May 15 00:11:53 bionic-copy notification-ar[1641]: GDBus.Error:org.freedesktop.DBus.GLib.ErrorError: Method invoked for RegisterStatusNotifierHost returned FALSE but did not set error
/var/log/syslog:May 15 00:12:15 bionic-copy pulseaudio[1597]: [pulseaudio] bluez5-util.c: GetManagedObjects() failed: org.freedesktop.DBus.Error.NoReply: Did not receive a reply. Possible causes include: the remote application did not send a reply, the message bus security policy blocked the reply, the reply timeout expired, or the network connection was broken.
and as the result Blueman bluetooth manager can't start on restored system.
But let's get back to your question.
I can reproduce the behaviour with SystemBack 1.9.4 on Ubuntu MATE 20.04 LTS.
The main problem here is the D-Bus:
$ cat .xsession-errors | grep -i error | grep -i dbus
(caja:1361): Gtk-WARNING **: 00:30:31.898: Failed to register client: GDBus.Error:org.gnome.SessionManager.AlreadyRegistered: Unable to register client
(caja:1804): Gtk-WARNING **: 00:30:34.858: Failed to register client: GDBus.Error:org.gnome.SessionManager.AlreadyRegistered: Unable to register client
...
$ sudo grep -ir error /var/log/ | grep -i dbus
/var/log/syslog:May 15 00:29:13 focal-copy pulseaudio[911]: GetManagedObjects() failed: org.freedesktop.DBus.Error.NoReply: Did not receive a reply. Possible causes include: the remote application did not send a reply, the message bus security policy blocked the reply, the reply timeout expired, or the network connection was broken.
/var/log/syslog:May 15 00:30:31 focal-copy notification-ar[1380]: GDBus.Error:org.freedesktop.DBus.GLib.ErrorError: Method invoked for RegisterStatusNotifierHost returned FALSE but did not set error
/var/log/syslog:May 15 00:30:52 focal-copy pulseaudio[1038]: GetManagedObjects() failed: org.freedesktop.DBus.Error.NoReply: Did not receive a reply. Possible causes include: the remote application did not send a reply, the message bus security policy blocked the reply, the reply timeout expired, or the network connection was broken.
/var/log/apport.log:ERROR: apport (pid 1785) Fri May 15 00:30:34 2020: debug: session gdbus call: (true,)
/var/log/apport.log:ERROR: apport (pid 1838) Fri May 15 00:30:35 2020: debug: session gdbus call: (true,)
...
For Ubuntu MATE 20.04 LTS I see one possible error in file-system restoration. Please compare two file listings below - first is from original system, second is from cloned (with SystemBack) system:
mate@focal:~$ ls /media/mate/original-system/ -al
total 1722520
drwxr-xr-x 19 root root 4096 May 14 23:13 .
drwxr-x---+ 4 root root 4096 May 15 00:38 ..
lrwxrwxrwx 1 root root 7 May 1 15:11 bin -> usr/bin
drwxr-xr-x 4 root root 4096 May 14 23:53 boot
drwxr-xr-x 4 root root 4096 May 1 15:11 dev
drwxr-xr-x 136 root root 12288 May 14 23:57 etc
drwxr-xr-x 4 root root 4096 May 14 23:57 home
lrwxrwxrwx 1 root root 7 May 1 15:11 lib -> usr/lib
lrwxrwxrwx 1 root root 9 May 1 15:11 lib32 -> usr/lib32
lrwxrwxrwx 1 root root 9 May 1 15:11 lib64 -> usr/lib64
lrwxrwxrwx 1 root root 10 May 1 15:11 libx32 -> usr/libx32
drwx------ 2 root root 16384 May 1 15:06 lost+found
drwxr-xr-x 4 root root 4096 May 14 23:48 media
drwxr-xr-x 2 root root 4096 May 1 15:11 mnt
drwxr-xr-x 3 root root 4096 May 14 23:21 opt
drwxr-xr-x 2 root root 4096 апр 15 14:09 proc
drwx------ 3 root root 4096 May 14 23:54 root
drwxr-xr-x 2 root root 4096 May 1 15:30 run
lrwxrwxrwx 1 root root 8 May 1 15:11 sbin -> usr/sbin
drwxr-xr-x 2 root root 4096 May 14 23:14 snap
drwxr-xr-x 2 root root 4096 May 1 15:11 srv
-rw------- 1 root root 1763758080 May 1 15:06 swapfile
drwxr-xr-x 2 root root 4096 апр 15 14:09 sys
drwxrwxrwt 7 root root 4096 May 14 23:57 tmp
drwxr-xr-x 14 root root 4096 May 14 23:10 usr
drwxr-xr-x 14 root root 4096 May 14 23:15 var
mate@focal:~$ ls /media/mate/SB@/ -al
total 160
drwxr-xr-x 24 root root 4096 May 15 00:20 .
drwxr-x---+ 4 root root 4096 May 15 00:38 ..
drwxr-xr-x 2 root root 40960 May 14 23:53 bin
drwxr-xr-x 3 root root 4096 May 15 00:02 boot
drwxr-xr-x 2 root root 4096 May 14 23:58 dev
drwxr-xr-x 136 root root 12288 May 15 00:23 etc
drwxr-xr-x 4 root root 4096 May 15 00:24 home
drwxr-xr-x 136 root root 4096 May 14 23:53 lib
drwxr-xr-x 2 root root 4096 May 1 15:11 lib32
drwxr-xr-x 2 root root 4096 May 1 15:11 lib64
drwx------ 2 root root 16384 May 15 00:18 lost+found
drwxr-xr-x 3 root root 4096 May 15 00:23 media
drwxr-xr-x 2 root root 4096 May 1 15:11 mnt
drwxr-xr-x 3 root root 4096 May 14 23:21 opt
dr-xr-xr-x 2 root root 4096 May 14 23:58 proc
drwx------ 4 root root 4096 May 15 00:28 root
drwxr-xr-x 2 root root 4096 May 15 00:02 run
drwxr-xr-x 2 root root 12288 May 15 00:28 sbin
drwxr-xr-x 2 root root 4096 May 15 00:03 snap
drwxr-xr-x 2 root root 4096 May 1 15:11 srv
dr-xr-xr-x 2 root root 4096 May 14 23:58 sys
drwxrwxrwt 7 root root 4096 May 15 00:32 tmp
drwxr-xr-x 14 root root 4096 May 14 23:10 usr
drwxr-xr-x 14 root root 4096 May 15 00:03 var
Please note the symlinks in the first listing. Since 19.04 they should be here.
The second strange thing is that SB@ has /root/.dbus/sessin-bus folder.
So there is something wrong on SystemBack side. If you are a developer of SystemBack - please carefully analyze the information above and try to fix this in the source code. Also I suppose that other Ubuntu flavors affected too as D-Bus is a core and essential component of all current systems.