Hi Martin,
many thx fr your reply. Good to know that other people are facing similar problems (is it just me or…). 
I am working under Win10 though using Unity 2021.3.16f1 (LTS)
After finding some feedback on Stackoverflow I managed to pull this off (similar to your approach):
- Download the current NuGet MongoDb driver
- Copy all .net Standard 2.0 version of the DLLs into a Plugin folder in my Unity project.
It seems to be working but now Unity is crashing quite often so I am not all that content yet. I will have to investigate the cause from the logs - will report if anything seems connected to the driver.
Many thx again
Scheuni