Thought I would let you all know in case you have missed it. A few days ago Postgres support was finally merged into Sonarr dev branch (meaning 4.x version). I have already transitioned to it, so far it runs without issue

You can mostly follow the same instructions as for Radarr from here: https://wiki.servarr.com/radarr/postgres-setup

I used the following temporary docker container to do the conversion (obviously replace stuff you need to):

docker run --rm -v Route\to\sonarr.db:/sonarr.db --network=host dimitri/pgloader pgloader --debug --verbose --with "quote identifiers" --with "data only" "sqlite://sonarr.db" "postgresql://user:pwd@DB-IP/sonarr-main"

When it completed the run, it outputs a kind of table that shows if there were any errors. In my case there were 2 tables (cant remember which ones anymore) that couldn't be inserted, so I edited those manually afterwards, so it matches the ones in the original DB.