Muppet Verse?

https://mattkprovideo.com/2019/06/17/muppet-verse/

Random Sesame Street thought(s)

We can assume that The Sesame Street characters and The Muppet Show characters live in a shared universe. After All, Kermit the Frog is in both right? And they were both (co) created by Jim Henson, right?
Big Big showed up on The Muppet show in the 70’s.

Did any of the other Sesame Street characters show up on the 70s Muppet Show? Did they show up on any of the other later Muppet TV Shows? I know Big Bird has a cameo in the first MUPPET MOVIE:

And (almost) all of the Sesame Street muppets show up in the wedding scene of “THE MUPPETS TAKE MANHATTAN.” ( 1984)

And there is the marvellous “Muppet Family Christmas” ( 1987) With most of the muppet characters interacting with Sesame Street Characters and the Fraggles!

But here is a thought that is buzzing around my head:
I’ve always assume that the Muppet Theater is supposed to be somewhere in New York City. They never said that, I just assumed its in some weird off Broadway theater where vaudeville never died. And its NOT a TV show to THEM…. its a live weekly vaudeville show….. we never see TV cameras in the Muppet theater do we? They maybe did that on later versions of the Muppets but that wasn’t in the 70s original was it?
If they’re in a shared universe, theoretically Miss Piggy could leave the Muppet theater and walk down to Sesame Street and get something at Hoopers Store…. and interact with the other Sesame Street denizens, right?
BUT….
On the Muppet Show Miss Piggy says to Big Bird : “Aren’t you on that cute childrens show with the puppets?”
So that means that within the world of the Muppet Show, Sesame Street is NOT REAL but it’s just a TV Show and Big Big is just an Actor on the show. So perhaps Miss Piggy could travel to the TV studio where they shoot the show, but its not real.
And in the Muppet Movie, Big Bird tells Fozzy Bear ” I’m going to New York City to try and break into Public Television!” So again, this shows that Big Bird is an ACTOR on a SHOW called Sesame Street, The Street itself isn’t real to the Muppets.
Which brings up other thoughts….
On the original Sesame Street that I grew up on in the 1970’s …. Kermit the Frog was not ON Sesame Street. He was a TV newscaster in skits on almost every episode… but he was never ON the street was he? Did we ever see Kermit talk to Big Bird, Oscar, the Humans or any other characters? The same with Grover, Bert & Ernie and the Count. Grover was only seen in the restaurant with the rude customer and sometimes with children. Bert & Ernie were only ever seen in their apartment…. we never saw them outside it did they?

The Count was only ever seen in the room of his castle, never ON the actual Sesame Street was he?
I saw them all together in the movie “Elmo in Grouchland” but that’s not the same as seeing them on the show. Do they show them all together on the TV show now?

And then theres THIS, proving that Sesame Street is in the Star Wars Universe:
RD-D2 and C 3PO visit Sesame Street.