Been using FAM for years.  FAM to PS, never an issue.  PS to FAM, no issue but when you reimport back into PS be careful, you have to delete all the original assets in PS or you'll have duplicates.

Re your question - FAM does not import from 2021 PS to 2022 FAM.  It can import from 2022 PS so roll over the client and then import.  Or, if not many assets, just enter them new in FAM.

Tried once to go from Excel into FAM. Never got the mapping done correctly.

Also, make sure you have the proper directories set up in FAM and in PS.  You need to tell each program where to look for the data.