Nope.
That was a total failure.
So, apparently, I can only implement reCAPTCHA stuff with a v2 key infrastructure. Well, v2 keys can't be created anymore, only v3. There may be a way I can enable it site-wide rather than on-call for registration, but I think I'd need some help to achieve that.
If anyone understands what to do, reach out to me. For the time being, it's back to the old way and denying 4+ bots a day, I guess.