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There isn't a setting for it. So, the retention is as long as the database has space.
I've seen a feature request for this, some instance claims it'd make a difference for their storage management. I doubt inbox storage would be a big factor here though.
Long term I imagine it’ll become an issue yeah?
I'll be real with you: I've had a look at the database schema and tables exactly once. It's a bowl of spaghetti in there. We just sort of view it as a single entity and don't really separate it out in any granular view.
What I can tell you is that the bulk of the storage is federated content. When a user subscribes to a community on another instance, the aussie.zone database caches content from it here for them. So, lemmy.world for example uses a lot more storage than the user messages. Or aussie.zone content if I'm being honest. We really aren't that big an instance. We are pretty engaged though. Our user base is small but active.
I can see that changing. Low quality content tends to be deleted when it's public and ignored when it's sent to a private inbox. Over time, that tends to result in a build up of junk.
Look at email for how bad private messaging could get.