Gamifiying iNaturalist has been suggested many times over the years, and aside from some small concessions (eg leaderboards) it’s something iNaturalist has resisted and I think that is for the best. Perhaps I’m wrong, but I think iNat’s strength is that the people who use it are motivated internally and really want to help others and create strong data.
Personally I dislike adding game elements to a pursuit - enjoying nature and helping others with IDs - that should be enjoyable (or at least internally compelling for us compulsive types) in and of itself, so I would be strongly against any sort of additional badges or incentives here. I’m not against them in principle - I love getting them when playing video games, for example - but I don’t think they will improve iNaturalist. If you want to earn badges for finding organisms, Seek by iNaturalist is a good alternative.
Those badges are related to the forum and come from Discourse, not iNaturalist.