This is rather weird.

I have seen warnings before not to upgrade to 21.04, but then I saw it is supposed to be fixed and affected only old hardware anyway.
I did the upgrade because Ubuntu (packet manager?) recommended it with one of the usual popup messages on the desktop - not by forcing it.

This is running in a VirtualBox, on some i7 8 core / hyperthreads machine, 2 cores assigned to VM.

The upgrade ran for 10 mins or so, but did not complete. It said something about something not working and some part being rolled back - I unfortunately did not screencap that. It then ended with a success message. I queried the Ubuntu version, and it's 21.04.
So far, so good, it seemed.

Until... the next time I fired up the VM.
Ubuntu starts until the desktop, well sometimes it gets to show the default background image, sometimes it only shows purple.
But there are no icons on the left, extept the lower left "3x3 dots square" menu button.
Nothing works.

Weirder still is:
If I completely kick that VM, and tell VirtualBox to "start without GUI", so it will show only a thumbnail of the desktop in the right upper corner of the VirtualBox main window, updated every 1 second only - then it does boot into the desktop.
And if I then "show", I can actually open a terminal and type commands, although the screen update is plagued by flickering - this is not the normal way to use a VM I guess.
The normal way to sart up the VM still results in the desktop not working.
I can only guess that the difference is some timing, or, the lower screen resolution (1024x768) of the virtual monitor that VBox presents to the Ubuntu VM when it tis started in this "without GUI" way. (without GUI seems to just mean that VBox does not open an extra window for the virtual monitor, with all the keyboard/mouse capturing stuff etc)

So I *can* get access to a console on that broken Ubunto, at least.
I tried to update + upgrade, which then caused a complaint about a broken /etc/postfix/main.cf file.
When correcting the badly inserted (not by me...) myhost name there and ran upgrade again, the thing would put in a bad name with two ".." at the end after the actual name, again, ...
So I made a backup of main.cf and blanked it, and let postfix create a default value filled one.
Then I ran upgrade again, this time it complete without complaints.

But the issue outlined above persists.

So. Does anybody have an idea what I could do to find out what is actually wrong?

It's interesting enough that resolution / timing differences make the difference of the desktop starting in a working manner or non-working.
Is that already a clue?

Ok - I went to virtual box settings for the VM, and doubled the default and previously working 16MB of video memory to 32MB, and also I saw a warning by virtualbox that another (not recommended) video controller than VMSVGA was set, so I changed it to that.

Now it works, so far. Interesting that there are no complaints by the system about not enough memory or such.