Generally the concept of the multiverse is a possibly infinite collection of universes of identical composition that only differ because of alternate choices its inhabitants make. So was there any in-universe explanation as to why in the MCU there are parallel universes that agree in form, but not in substance? In other words why do the universes all have a Peter Parker, an Aunt May, a Spider-Man, and presumably an Electro, Dr. Octopus etc, but they are all actually different people in each universe?
As we see in Loki, there’s a universe (or possibly just a timeline, although that’s probably over-complicating things) where Loki is blonde and female (plus one where he’s an alligator). And as we see in Doctor Strange and the Multiverse of Madness (very mild spoiler):
there’s a universe where everyone and everything is made of paint.
Apparently in Marvel’s multiverse, someone can have the same name and abilities as someone in the universe we’ve been watching, but have a different physical appearance, which makes just as much sense as anything else multiverse-related.
Your interpretation of the multiverse is not correct or doesn't explore the full range of possibilities.
Generally speaking infinite choices make infinite possibilities and that opens the possibility for the writers to write any story changing anything. In that sense, in universe, Miles Morales as Spider-Man is a clear indication as it is all the different variations of Spider-Man (and other heroes) on the multiverse, where Spider-Man is not Peter Parker (or vice versa).
Note not ALL universes have an Electro or a Miles Morales. In fact in the other universes there's an explicit mention that there is no Avengers. It is made explicit in the movie that certain villains have not appeared in certain universes, Electro not being present in the Tobey Maguire OR Tom Holland universe.
While this is not specifically stated in the movie it is clearly hinted by the fact that Aunt May never married. This means she never met uncle Ben and in fact it is made as a point in the movie for her to be the one that quotes the famous "with great power comes great responsibility".
If Aunt May never married or met uncle Ben, if follows that Richard Parker may have met someone different than Mary Parker. Furthermore, Mary or Richard parents may have been different, therefore making the physical appearance of Peter Parker completely different.
Obviously this is an in universe answer. Given the fact there are infinite parallel realities (as each reality is formed by a branch in decision), that in itself justifies that there're infinite possibilities to chose from, including the ones that are chosen by the writers.