OP is just asking why they a third party mastodon app can’t login to a Lemmy or kbin server, which is a valid question.
From an authentication standpoint there’s no reason for their auth flows to be at all different or use different endpoints relative to their domain.
The returned profile or account object might have different fields which could cause an app to crash, but there’s no reason for every fediverse app to not use some of the same basic schemas and endpoints.