Ok, I think we can close the issue… But I do not have any explanation for it.
I downloaded APK from Bitwarden Git repo (both an f-droid and normal versions).
So I removed the GooglePlay version and installed one from Git (non f-droid => com.x8bit.bitwarden.apk) and restarted my BitRS service…
And magic happened - it now syncs with no issue!
P.S. It may help others I think =)