I am getting an error message " authentication method 10 not supported" while trying to create stanza on postgres14 after upgrading postgres from v.10 to Postgres v.14.
I am using pgbackrest version: v.43 and the scram-sha-256 for hba authentication.
This sounds like your libpq is too old, and is not related to backrest itself.
Make sure you have libpq of at least version 10 as well, and not just the server. (Exact package name will of course depend on what distribution you're on, which you didn't specify)