Just checked out OsmAnd and managed to blow through the “free” downloads just downloading the maps local to me

On the Play Store version, you're able to download seven offline maps, where a map is either (your choice) a country or a state/province/etc. (some smaller countries don't have the state/province/etc. level and just give you the whole country). I haven't pushed it, but I think you should be able to have seven countries(?) available for offline view (maybe the world map counts as one, so six?).

It’s a bit off-putting that they’re charging for open source data, unless I’m missing something…

OsmAnd is a BV (besloten vennootschap, effectively an LLC), so similar to something like ProtonMail, there's a "Start" (free) tier, a "Maps+" one, and a "Pro" one, where both paid tiers unlock unlimited offline map downloads. (You're able to use online maps as much as you want.)

The maps are stored on and downloaded from OsmAnd's site in a .obf file, which is OsmAnd's own format. So they're essentially charging for open-source data that they've converted and are hosting as a way of incentivizing users out of the free tier, which as far as businesses go, I see no real problem with. They're making that open-source data more accessible with a powerful app and making features that encourage people to contribute back to it, not parasitizing it.

OsmAnd, to my understanding, is well-liked among OSM's contributors for having a great app and a healthy business model.

Anyway, with that out of the way, the "Maps+" and "Pro" features are free on F-Droid. It is, after all, free and open-source.