Is there any real way to recover deleted messages on Messenger, or is that gone for good?

Honest answer: no in-app undo, but two legit places to check. 1) Archived, not deleted: open Messenger, search the person's name, sometimes it was only archived and reappears. 2) Download Your Information from Facebook (Settings > Your Facebook Information > Download Your Information > Messages). If the messages existed before deletion they may be in that export. Once truly deleted from both sides they are generally unrecoverable, and no third-party app can pull them back.

The Facebook data download is the only real shot and it is worth trying. It takes a while to generate but your history is often in there.

Check Archived first (search the name). Half the time people 'deleted' a chat they actually just archived.

Avoid every app advertising 'recover deleted Messenger messages'. They cannot reach Facebook's servers, they just want permissions or money.