For those that have seen it do the additional, extended scenes feel naturally edited in or shoehorned? Is the original cut smoother?
Borrowing from The Caped Knight who succinctly explained nearly all the extra footage and giving comments:
Peter getting interrogated by Damage Control and the pattern that Spidey battles involved historical landmarks & May insulting the damage control agent
-The "landmark" bit may have been intended to set-up Jameson's comment about Tom!Peter "about to destroy another national landmark" but I do think it was nice means of acknowledging continuity within the 3 MCU Spider-Man movies.
More of Midtown high including Peter wall crawling in gym class
-I think these scenes should've been included in the original theater cut, simply because they help flesh out Tom!Peter's post-identity reveal and the discomfort with his newfound fame. We get more reactions from students to Peter, with some taking interest in him (where they wouldn't have before), others just commenting "hey, I've been in class with him", and others curiously observing him. The bulk of Flash and Betty's screentime were cut out with these scenes. There is one part that should absolutely have remained as a bonus scene, and that's a scene of Betty's reporter channel where she's interviewing various people (Flash, Peter, Ned, teachers). It went on for too long and felt kind of awkward (though the awkwardness may have been intended).
Spider-Man stopping the robbery played by Harry Holland (Tom’s younger brother)
-Again, mostly a scene to help flesh out post-identity reveal Peter, but I did like that this was basically an inverse of Homecoming where "friendly neighborhood Spider-Man" Tom!Peter is no longer being treated as such. He stops the robbery, but there are a few civilians present who all have mixed reactions to his help; one chastises him, one defends him, and the person who was being helped wasn't necessarily appreciative (or I don't remember him thanking Peter directly).
More clips from J.Jonah Jameson
-There were two new Jameson scenes I could recall, which include an additional report on Spider-Man leading into Betty's "go get 'em tiger, or should I say, spider?" right before Peter/MJ/Ned go to Midtown High (Betty in the original cut has a longer report before the go get em tiger line as a result of Jameson's scene being cut), and Jameson actually reporting on the Electro/Sandman incident on a tip from one of the construction workers at that site that's right before he advertises his Daily Bugle supplements. The construction worker's tip did not present a wholly negative picture of Spider-Man, hence explaining why Jameson would be insistent on one of his news people follow after Peter to get "incriminating footage of Spider-Man". More Jameson isn't a bad thing, even if this version isn't as fun as the Raimiverse Jameson.
The elevator scene cleaned up
-This scene being cut is understandable, but they smash cut into this scene (like the scene of Dr Strange shutting out Peter from the sanctorum post failed spell) after Electro's "If this goes south, I'mma fry you from the inside out" line so I found it amusing enough that I wouldn't have minded if they kept it.
Matt Murdock defending Happy
-Not much more Murdock screentime or lines. He is defending Happy in front of Damage Control by saying he's innocent and tells Happy "do not sweat". The only notable thing is Happy getting a camera notification on his phone showing Peter/May/Villains entering his condo which helps explain his later phone call/voicemail to Peter, though that wouldn't be difficult to infer.
A longer conversation between Peter Parker, Peter and Peter Benjamin Parker at the Statue of Liberty
-I would say this is where the original cut is better; the longer conversation on the same topics (Tobey!Peter's web situation and supervillains) did not flow as smoothly. The only thing I found somewhat awkward in the original cut was Tom!Peter going into supervillain talk because it felt like a "we need another topic to talk about" kind of line. In the extended version, this line was the result of him actually trying to steer the conversation away from the subject of Tobey!Peter's web situation after Andrew!Peter was making it too awkward (Andrew!Peter had a line that went something like "I'd like to see those holes" concerning where Tobey!Peter's webs come out from and Tobey!Peter gives him a WTF look), giving it a more sensible transition. One notable thing is Andrew!Peter having a line about "wishing to do things differently" right after talking about Max being the sweetest guy ever and "second chances", but I imagine it was cut because of redundancy; Tobey/Andrew would figuratively get their second chances in a "show don't tell" manner through their actions in the Statue of Liberty fight.
Alternate end credit scene with Peter Parker missing from Betty’s recap of the adventures of the trilogy featuring Midtown high classmates
-Some clarification; the highlights featured in Betty's recap still feature Peter Parker, but in some of them his face is obscured (a picture of him in the Far From Home Europe trip for instance has a bird completely cover his face), in others he is only partially in frame (showing his arm), and then some highlights outright remove him. So Strange's spell, at least where it comes to physical evidence, is somewhat imperfect - it doesn't completely erase Peter Parker from physical evidence, but it does just enough to ensure that no one will pay attention to his existence. This could partially help explain Peter being able to rent and move into an apartment; some form of his identity is probably still in-tact in a manner that helps him, such as his social security number.
The one scene Caped Knight didn't mention was a extended scene in the Undercroft when Peter/Ned/MJ are doing preparation before hunting down multiversal visitors. The "Monster Mash" song is playing over this scene instead of the "wizard-y" sounding MCU Spider-Man theme, and this extended version is a mostly comedic scene with Ned making a mess knocking over stuff by accident. Probably better off as a bonus scene, like Betty's news channel.
tl;dr Overall, I'd say that none of the extra scenes felt shoehorned in; I think they were edited into the movie in a way that it helps flesh out the movie/set-up/explained some things more, but there were definitely some extended scenes that were better off removed/cut down/made into bonus scenes. If the Tobey vs Goblin fight was added to this extended cut, I would consider that a form of shoehorning, but it would be really neat fanservice (in a movie that already features a lot of fanservice, what's one more bit of fanservice)