No, Marvel's Spider-Man 2 won't be co-op

techradar.com:

Marvel's Spider-Man 2 is due to release later in 2023, and Insomniac has responded to a tweet from a fan to confirm that the game won't have a co-op mode, after days of speculation that the upcoming action adventure would be bringing multiplayer into the mix. 

The rumor started after comments made by Nadji Jeter, the actor that plays Miles Morales, at SacAnime last September surfaced recently, when he was asked whether Marvel's Spider-Man 2 would have co-op he responded: «I believe it has been announced, I don't know if it's been announced or not but I think so.» (via VGC)

Watching it back it does seem to be a misunderstanding on Jeter's part, as he mentions saying that he isn't sure on whether the co-op has been announced and then saying that he thinks it has been announced, however comments afterwards do muddy the issue slightly. 

Nope! It is an epic single-player adventure!May 22, 2023

Regardless, fan speculation ramped up, especially as Marvel's Spider-Man 2 is expected to appear at this week's PlayStation Showcase on Wednesday (May 24). It fits with what's shown of the game, too. While 2018's Marvel's Spider-Man was a solo adventure, the Spidey sequel is due to feature both Peter Parker and Miles Morales.

Tony Todd, the Candyman star who is voicing Venom in Marvel's Spider-Man 2, earned himself a slap on the wrist back in March for getting too excited on Twitter and revealing that the game was planned to drop in September 2023. He soon deleted the tweet — presumably after a terse call from Disney — and said he wasn't sure when Marvel's Spider-Man 2 would actually be launching. 

Still, while there may not be co-op in the upcoming action adventure game, Insomniac is also still working on a Wolverine title. Maybe fans will