A potential angle to explore in terms of connecting Spider-Man more to mutants as a supporting cast who don't detract from him being the center of HIS stories.....is Peter inquiring about the status of various mutants, now that mutant resurrection is common knowledge.
Throughout the seventies, eighties and nineties, Spider-Man comics were actually the single most likely place to see mutants outside of the X-books.....with the distinction that these were usually mutants created just to be one-off appearances in his books. Like, being a mutant WAS an easy way to explain a character having powers if you didn't want to spend a ton of your available pagetime crafting a backstory for how this random side-character in an issue came to have powers (that are usually tied into the issue's plot, or necessary for it to work). And so there are a lot of random, obscure mutant characters who never appeared anywhere outside of one or two Spider-Man adventures....some were minor criminals, some were runaways or kids being exploited for their powers, some were victimized by their own powers and with Peter trying to save them from themselves even.....
With the other common thread most of these minor mutant characters shared.....being that most of their appearances ended in tragedy. There's TONS of obscure mutant characters who basically only existed to contribute to the pathos and angst that's defined Peter at many points throughout his existence. In some cases, it was because the mutant guest star died tragically and Peter blamed himself for being unable to save them.....in a couple notable instances, they were destroyed by their own powers or lack of knowledge about how to safely use their powers, with Peter wishing he'd been able to help them in time or get them the help they needed to avoid that fate.....and many of the minor mutant criminals or henchmen he fought were detailed by the narrative as being impressionable mutants who were manipulated or coerced into crimes from a young age, with Peter reflecting on the tragedy of that and wondering at times if that could've been him if he'd encountered the wrong villain before he started as Spider-Man or when he was in a particularly vulnerable period or mindset.
Point is, Spider-Man writers LOVE pouring on the angst with Peter. One of the most popular moods for writers to inflict on him, at many points in the comics, has been 'how can I maximize Peter's tendency to beat himself up for things he thinks are all his fault or he should've done better....I know! tragic mutant guest star Peter fails to save or steer away from jail or a life of crime or that refuses to trust Peter and let him help them.....leaving him angsting about the unfairness or futility of it all in the aftermath, as he perches on a rooftop in the middle of a thematic downpour because he deserves to feel like a drowned rat, sitting inside all warm and dry is for closers, not superheroes that couldn't stop random NPC gang leader from shooting the mutant guest star who ran away from home only to wind up having their powers exploited by some random crime lord wannabe looking for his meal ticket.'
Plus, there's this really weird mini-trend of major Spider-Man villains having derivative characters created to take up their mantle/identity when they're temporarily dead or unavailable to writers....and with these stand-ins often being mutants for some reason. It happened with one of Kraven's kids, there was a mutant named Francis Klum who used the Mysterio identity briefly, there was a mutant stand-in for Chameleon once.
Anyway - point is, lots of minor mutants have been used in Spider-Man stories in past decades, and almost always for one specific purpose - to have their story end tragically and make Peter feel like shit.
And yeah, most of them are dead, lol. The big names like Shriek, the stand-ins like Kraven Jr. and NotMYMysterio, the really obscure ones like Mindworm.....they all bought the big one, winding up gristle for Peter's 'Dear Diary, Fucked Up Again' monologues.
So! Think how uplifting it could be for Peter - who uh, is not having a lot of super great days, currently - to upon finding out about mutant resurrection.....ask his friends like Bobby and Angelica to ask around about various dead mutants he's probably got listed in a journal somewhere under the heading "People That Would Be Alive If I Were A Better Superhero w̶h̶y̶ d̶o̶e̶s̶ e̶v̶e̶r̶y̶o̶n̶e̶ k̶e̶e̶p̶ a̶s̶k̶i̶n̶g̶ i̶f̶ I̶'v̶e̶ t̶r̶i̶e̶d̶ a̶n̶t̶i̶d̶e̶p̶r̶e̶s̶s̶a̶n̶t̶s̶." Give him the opportunity to get some closure with one or two mutants whose encounters left him with a buttload of unmerited guilt, as they impress on him that it wasn't his fault, they never blamed him, and they appreciated everything he did or tried to do and never hated him or thought he should've done more. Let him shed the load some of these mutants' deaths left on his shoulders as he's reassured that they got a second chance at things after all, and they're actually doing pretty great now.
Peter's the perfect opportunity to showcase a non-mutant who's just fucking HAPPY about mutant resurrection, not needing it to have anything to do with him or any other humans, because he sees clear evidence of the value it holds for mutantdom in letting them change the fates of random mutants he himself saw get screwed, while being unable to do anything about it himself. Like yeah, sure, it'd be great if everyone who died tragically got a chance to come back, but just because its not universal doesn't mean that he doesn't still see it as a good thing every time its been used to give a second chance to a mutant he totally agrees got dealt a shitty hand and deserved a better end to their story. He can mourn the loss of lives not brought back while seeing ones who ARE brought back as still having value, and the very fact of their returns being something to celebrate or find joy in. Its not an either or, everyone brought back or no one at all. There's room for space in between. Peter's a guy who's good at seeing room for nuances and space between the lines - at least when it comes to other people.
And then too this could also pave the way for some of these minor or lesser known mutant characters to segue into future Spider-Man stories. Maybe some are touched that Peter checked up on them or still cared enough to remember or think of them after all this time, and they ended up staying in contact with him or offered their help if he's ever in a bind. And most of them would fit all the qualifications Gray Lensman laid out, and which I think are well reasoned.....they tend not to be so powerful as to take over Spider-Man stories or render Peter's own contributions useless, they usually aren't well-known or high profile in their own right and so wouldn't detract from his star power in his own titles, but would only benefit from it, much like any other supporting cast.....most of them have REASON to view Peter favorably and be actual supportive presences in his stories where he tends to have more than enough detractors already....and their very existence, or resurrections, could help remind Peter even when he's smack in the middle of one of his Bumming Hard eras, of how radically things can change or turn around, no matter how hopeless or useless or unfair things seem at a given moment.
I mean, even a character like freaking
Mindworm would be a total mood-lift for Peter if he were to find out he was brought back.....and Krakoan resources could help William have a much greater control of his powers than he ever did in his original lifetime, and with that control and understanding of them, as well as being able to skim from Krakoa's psychic/life-force reserves the way Selene and Emplate do, he'd not only be much healthier and without the contributing factors that catalyzed most of his violence in the past, he'd likely be a lot more self-assured and resistant to being manipulated or influenced towards villainy as well. Heck, with a healthier, stabilized physiology, training with his powers, and a second shot at life starting from a relatively blank slate.....just give him a new name and I could see him being for Peter what Porcupine was for Jessica Drew in one of her recent solo series, if people get that reference.