I managed to fix it. For future generations, here's what I did:
Turned out I needed to start the device in safe mode and let Sierra finish its installation - sorting out whatever incompatibility there was automatically. I did try safe mode, but when it showed exactly the same behaviour - a frozen bootup screen with nothing happening - I gave up after 15 minutes and restarted the machine.
Luckily, I then decided to try safe mode and verbose mode at the same time. To do this, I logged into the recovery console (Cmd + R during bootup), started the terminal, and enabled both modes using
sudo nvram boot-args="-x -v"
(this does not seem to work when booting the machine in Single User mode because of sandbox restrictions; it has to be the terminal in the recovery console)
With this, I managed to see on startup that while the boot screen would be frozen for a long while in safe mode, too, a lot was happening behind the scenes, and eventually I got through to the login screen.
After logging in, the Sierra installer worked for another while (the installation was not yet complete) and rebooted.
(For the record, at this point, I also removed an extension named SteerMouse - but I don't know whether that was what caused the problem. On its website, it does claim to be ready for Sierra.)
Once I was logged in again, I opened a terminal (from within MacOS now, no need for the recovery console) and turned off safe mode and verbose mode again:
sudo nvram boot-args=""
the system is now booted up in normal mode, and everything seems fine.
I got a new compatible SSD, fresh installed Catalina, and everything worked fine...Then I proceeded to restore the system from a TM backup...The problem is that when the system boots...loads really slow in the last 1/3, and then after it seemingly fully loads, it gets stuck there.
This is key. If after a clean install everything is great but you subsequently restore from Time Machine, you may have a corrupted backup from the failing drive.
Instead of a restore, try doing a data migration Using Migration Assistant instead. This will copy over your data and settings over but leave the OS untouched. I prefer this method especially when upgrading to a new OS.
Best Answer
Had the same issue and found the solution here: https://discussions.apple.com/thread/7787207?start=0&tstart=0
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EDIT: This worked for me. Note that I also had no sound but got it back after moving back "vecLib.kext" (by again returning to recovery mode and moving it back from the kextbackup-folder), so try to keep that in place from the beginning :)