Yes, BSD licenses are compatible with AGPL meaning BSD licensed code can be combined with AGPL licensed code while complying with both licenses. However, it does not give you permission to
relicense the BSD code (or derivative works) as AGPL. The author is free to license any new code they write as AGPL, however the license for the machine translated code is another question. If it is considered a derivative work (which I think it should be) then it must remain under the Postgres license.
If it is not a derivative work, then for copyright to apply at all then it must be an "original work" which has "at least a modicum" of creativity applied by malisper in the translation. If this is satisfied then malisper could choose any license for the translated code they want, compatible with Postgres or not. If it isn't satisfied then no license applies, because it isn't eligible for copyright - essentially it is public domain.
The safe and polite thing to do is to keep the same license when performing machine translation.