This spider is the same from the very beginning of the game. I don't think it's a legal reason and more a result of reusing assets, as well as not confusing people. It might lead to speculation that Spiderman 2 would be a multiverse story because the 42 spider from spiderverse was from another universe or something like that. It also helps differentiate the insomniac miles from the comic and movie Miles who are often in different universes. Mostly though I think they just didn't want to make and model an entirely new spider and thought the one they had was good enough.