davwheat I planned to do this, but the Extiverse API didn't provide this data I don't think.
It does, it is just less convenient than Packagist. For regular extensions it is probably better to use Packagist metadata directly (you can just pick first release from https://repo.packagist.org/p2/rob006/flarum-lang-polish.json) - it should be more efficient and data is always fresh. But for premium extensions you need to use Extiverse.
davwheat Packagist's data might be more up-to-date, but as far as I'm aware, it's easier to just use Extiverse on its own for simplicity.
In your case it probably will be simpler to use Extiverse only (only one implementation to fetch metadata). Although Extiverse has some rate-limiting that may be problematic in your use case, so I would check that - displaying badges for 61 different extensions may just kill your service.
If you have any concerns related to the Extiverse API just voice them in the discussion 
If you need less throttling, I can add something that makes it more lenient for you. If you need a shorter compatibility list I can introduce one too
The main thing that would be a massive help is to list the latest core version that the extension supports in the extension's details. From what I've seen, I think the only other way is to include versions in my request and check against the latest version, but I'd imagine it's a waste of bandwidth to include all the versions in the request.
We'll see if rate-limiting becomes an issue. Hopefully not, but who knows 
I might end up moving it off of my Pi if it's used a fair bit, too. 
It looks like https://flarum-badge-api.davwheat.dev/ is dead.
https://flarum-badge-api.davwheat.dev/ there is a 503 error
davwheat he/she was right. I saw that error too. Maybe you should set UptimeRobot.
I've got Upptime set up which uses GitHub Actions.
Looks like it did go down: https://status.davwheat.dev/history/flarum-badge-api
