That might be an etymological connection, I’m not sure. If you look at the って page, you’ll see that って can be short for many things, and many of them include と, but in this case I think it’s best to see it as just directly replacing は in very casual speech.
I appreciate that! I have come across the usage of って Of replacing は Before But there are so Many Things that ってCan Be used for, I over looked that. I have taken note and will look out for it more as that usage.
I always assumed that colloquial 「って」 came from 「とは」or「ということは」, which are full, formal ways of indicating “Hey, I’m speaking about the concept of ____, rather than literally that ____ over there.” The usage matches, as far as I know, and it lines up with 「って」 also being short for the 「と」 particle when quoting.
And if that’s the case, most of those seemingly different 「って」replacements are actually the same 「って」replacement.