So, here's part of the problem: For the longest time I suspected that the installer script wasn't cleaning up the directories before it installed to, and especially after it uninstalled.
After your note, I did a little searching, having used the installer to remove Parallels Tools from the VM just yesterday I assumed it would clear out the extra directories, but it didn't. The prl kernel extensions were still in all three kernel/extra directories. So I tried an experiment to re-install. Afterwards, only a few the extensions were dated 16 Oct, but there were a few there left over with a date of 15 Oct from yesterday, including prl_vid.ko.xz.
So I went through and cleaned house: Deleted all parallels_tools directories from /usr/src and cleaned out all of the prl extensions from the three active kernels' /usr/lib/modules/5.14.[9,10,11]-200.fc34.x86_64/extra directories. I also made sure nothing was in the weak-updates directories, because those used to be used. Then I ran the installer and checked to see what was done. It re-created just the /usr/src/parallels_tools-17.1.0.51516 directory, and only installed to /usr/lib/modules/5.14.11-200.fc34.x86_64/extra directory as shown below:
View attachment 18537
As you can see, nothing was installed to the other three kernels' extra directories and didn't even delete the uncompressed ko's.
Then I ran the installer again to finally finish the job.
View attachment 18538
It seems to be working, but I can't possibly be the only one with this issue. There are several reports of booting into an unresponsive black screen in the past, and this is the likely reason why. The installer script should delete all prl_*.ko and prl_*.ko.xz files prior to an install (and especially after an uninstall) to prevent these kinds of problems. Why I had to run the installer twice to complete the job is yet another story.
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