This is definitely the case (that tagged users in images are not part of the search index). Today, there’s no API support for tagging users in images on post, and there’s no indexing of those handles for search either. This partly stems from the fact that the free standard search API is ~11 years old and has not always been updated for all of the new features across the rest of the platform. I’d have to look into whether premium or enterprise search index those handles but I’m not able to say for sure right now.
You’re welcome to request features via the help form or via the roadmap category. We’re not able to make commitments to future API features beyond what is currently published in the roadmap, however.