(Note that at the moment, FAF can't access the data partition of an APFS clone, but the dev is working on a fix.)
For what it is worth, I just tested FAF 2.1.1 and it had no problem finding files on my desktop in Biq Sur (MacOS 11.0 beta) and Macintosh HD (Data) is among the twelve (count 'em — 12) real and temporary volumes FAF sees on the Big Sur boot drive.
Clarifying what I see and have communicated with FAF's dev about:
This screenshot shows what I see in /Volumes while booted into HD, and
this one shows what FAF 2.1.1 sees.
HDz and CCC are clones (the former in the same container as HD...the latter in a different container), but what FAF is seeing is only their system volumes. I can search their data volumes by selecting the appropriate volumes in /Volumes and searching "in Finder selection."