We've had great success with a custom gh action on a self hosted runner. It sets up codex and all the same stuff a dev has on their machine:

So dbs, seed files, etc, and then just a review prompt and some skills and a few scripts.

It triggers on a new published PR or if tagged @bot-name. It's way better than the other services we've tried (which was admittedly ages ago) because you can get it to work exactly how you want it and it's dead simple.

With Codex, for the time being at least, you can use a subscription, so it's basically free if you're already paying for one. But on API pricing it's still not too bad as it doesn't produce that much output.

I set this all up in about half a day. Codex does 99% of the heavy lifting.