The part where George tells Paul "I'll play anything you want or not play if that's what you want" was the most tense moment from the original "Let It Be" doc so that scene is basically extended, providing more context and IIRC, what prompts George to actually quit is Paul sternly telling him to stop playing while he's explaining an arrangement (didn't know about the cut scene of John and George though).
But yes, Paul's steering the ship. Already knew he was always the most technically accomplished and the most prolific songwriter but that really comes across. He basically tells the others that they can't just jam and wait for things to magically fall into place- at a certain point, somebody's gotta impose some structure. Every band needs a guy like that. Just a shame the others seem mostly uninterested.
"Across The Universe" is by far the best song on the album but was a "White Album" leftover and "909" was one of John's earliest songs so "Dig A Pony" was really the only new song John wrote for the album- and it's just an okay one. So the scene where Paul's basically saying "Hey, you written any new ones? We've got this deadline..." was interesting too.
Yeah having Yoko next to John the whole time was awkward but it's important to remember that it's what John wanted and insisted on. I'm sure Yoko was bored out of her skull most of the time.
"Let It Be" was another one Paul started during "The White Album" (is included on that recently released box set of the sessions) but he's finishing it in the doc and some random dude suggests the piano fill and of course doesn't get songwriting credit. Wonder how often that happened- imagine the royalties!
Folks are mostly focusing on Paul writing "Get Back" and yeah it's a great scene and recognizable/relatable to a songwriter like myself- it appears like you're channeling something, almost like you're trying to remember a song that already exists. Also notable that "Get Back" is a pretty simply songs- mostly a vamp on G, A and D major. Still impressive that he was able to pull it outta his ass but definitely not among their more sophisticated songs.