Indreksi unfortunately I have never seen that issue before so I am not sure.
Just to confirm, I assume Facebook login through the Facebook browser does not show that same error?
Could it be Google themselves who blocked the Facebook Browser 🤔 But I don't know of any method for webmasters to force mobile apps to open their website in a separate app. Usually it's only a setting in the app itself that the user has to know about and change.
If we know which user agent condition blocks login we could add a check for the same agent to generate a warning like you suggest.