OsmAnd+ installed from FDroid is 100% free AFAIK.

What about iOS?

There is no free option for iOS.

On F-Droid that is OsmAnd~, and it is indeed the free equivalent of OsmAnd+ from Google's app store.

I can get OsmAnd~ from FDroid for free.

You can also download map files from the server manually via, e.g., a web browser and get unlimited downloads that way. Don't need to pay for the standard functionality no matter where you downloaded the apk.

OsmAnd is free-as-in-beer if you want it to be, though imo that's not fair to the developers unless you truly can't afford a few euros (which can be, no judgement, especially in countries with lower incomes or high income disparity).

So how do they finance the servers from which you download the sizable map files, if there's no "pay to unlock unlimited downloads" like in OsmAnd?

"Our sponsors - Mythic Beasts ISP provides us two virtual servers with 400 TB/month of free bandwidth to help our users with maps downloads and updates."

On their github README.md.

Mythic Beasts are absolutely great, on that note. One of the truly old school hosts in the UK. They pay their employees a share bonus, they're technically excellent, and their services are reliable and well priced. I've been using them for years (since Bytemark got eaten by IOMart) and love them.

We pay it out of pocket or from users' donations.

Also consider that with Google you have to redownload your area of the map almost constantly since they're online maps, whereas it's only even possible to download a ~100mb map file from OrganicMaps monthly-ish when they release app updates and most people don't update. 100mb per user is nothing.