Haven't tried iNaturalist yet, but I love Merlin Bird ID [1] and Flora Incognita [2]. The latter seems to be exceptionally accurate (over 80% up to 98% depending on the dataset) [3]. They also expose an API for "registered external clients" [4], but so far I sadly wasn't able to find any further documentation on it.

A problem I often have with Merlin is that the birds seem to know when I record them, and promptly stop singing...

[1] https://merlin.allaboutbirds.org/

[2] https://floraincongita.com/

[3] https://doi.org/10.1002/pan3.10676

[4] https://doi.org/10.1111/2041-210X.13611