I'm mostly concerned about two things regarding this issue.
1. Is it possible that this error did/can do any 'damage' to prefabs or templates? I don't see any problems for now both in the play mode and while looking at the files (prefabs and templates) in the text editor.
2. Can I safely upgrade from 2019.3 to 2021.2 now before this error is fixed/solution is known? Is there any chance that this issue is somehow problematic for the update?
I have found this problem during the preparation for the update from 2019.3 to 2021.2. I always update Playmaker to the latest version before upgrading Unity (as suggested). Now the Unity upgrade is on hold because of this problem.
I could just upgrade Unity and check how it goes but my project has 200+ Playmaker templates and 100+ prefabs that use fsms/templates so I'm generally careful with plugin and editor updates to avoid situations when something wrong is found many weeks/months after upgrade.

BTW.
I've noticed that after this error happens during the build process Unity is re-importing some prefabs (prefabs which were preprocessed by Playmaker while building) after relaunching the editor.
Thanks