It seems like Noggin didn't edit Muppet inserts from Sesame Street Unpaved, but quite a few street scenes, that were part of the plot and not aired in other episodes that Noggin aired, were cut. Noggin needed to cut a few minutes from each episode, but I would think they'd cut material that appeared in other episodes that Noggin was airing (unless it was something they objected to airing). And I believe there are some inserts that were completely cut from Noggin (like "Ride a Bike" and Gordon taking a bicycle ride... two different segments with adult characters riding bikes, without wearing helmets).
But in looking at some of Muppet Wiki's guides for episodes that aired as part of 123 Sesame, Noggin did edit out some Muppet inserts. I had been aware for years (after seeing the episode on iTunes) that one episode removed some Baby Tooth and the Fuzzy Funk segments, and after seeing all the season 25 episodes now have full rundowns, I looked at the page for the episode where Big Bird looks for somebody is sad and saw that Noggin cut Harvey Kneeslapper's "A" joke (I had seen the episode on PBS and remembered there being a Harvey Kneeslapper segment in that episode). Clicking on the photo to see what episodes it links to, I don't think that one appeared in any other episodes Noggin aired (years before HBO cut Harvey Kneeslapper segments from whatever episodes he was in, though I think other Harvey Kneeslapper segments remained in Noggin episodes).