Last time when I had installed Trixie and configured it with raspi-config, I had at that time enabled VNC in the interfaces. I'm assuming it was running Wayland at the time, and enabling VNC then may well have installed Wayland-VNC. After rebooting, VNC was working, but picochess.service was hanging. Its status then was enabled, but it was inactive, and dead.
This time however, Tassos had found out that there was an issue with VNC, so I ran raspi-config without enabling VNC. I enabled X11, and pulseaudio, and rebooted the RPi. I then updated Trixie, and ran install-picochess.sh. This time picochess.service was enabled, active and running, confirming there's some kind of issue with VNC. I enabled autostart, and tested it. PicoChess came up and ran without issues. I then wanted to see what would happen when I enabled VNC, so I used SSH to run raspi-config. After rebooting just to be sure, I noticed that this time the status of picochess.service still was active, and running, but PicoChess was only displaying a completely white screen. I waited a while, and to my surprise PicoChess started properly, and VNC was working as well!
I now believe the difference is that the RPi was running X11 at the time I installed VNC. This probably resulted in installing the X11-version of VNC, so all was well, and everything is now up and running.
I've now read Johan's latest post as well, and the result of the commands he suggested is that the RPi is running X11, and vncserver-x11. Awesome job, guys!
BTW, I noticed prompts about the key ring. Apparently, this is caused by autologin, which I had configured as well. If you see the prompt, enter a blank password and confirm it. This will satisfy the key ring, and stop the prompts.