Passwords were imported from Google Chrome on Windows 10 in Firefox 102.0.1 (64 bit), then syncing...
Firefox 102.0.1 (64 bit) installed on Linux, syncing... result: imported passwords aren't available. When I added manually some logins and synced them, then the sync was successful.
After several experiments I decided to save passwords into a file on Windows and I imported them on Linux from the same file.
Unfortunately the above workaround isn't a solution when I move the the third, forth, fifth, ... machine and I use them simultaneously or alternately.
I found a solution here: https://support.mozilla.org/bm/questions/1268839
Copying below in case it disappears.
"I resolved this issue with the following steps:
It immediately auto-synced all passwords and then I reconnected the other machines, they synced as well.
I guess maybe there were some hiccups between devices... I don't know."