I also keep thinking about the use of Peter's sudden spurge of mutation amd his creating the universal Inhibitor and how Bruce warns him really early on that it could be used to suppress superhumans - and, of course, the way it gets used on Jean (and could be used on mutants) feels a lot like the Mutant Cure that was brought up in the original X-Men movies - and how it could be used in the MCU later.
(And I think it's important that mutation as used in Bruce and Peter's discussion covers any form of super DNA - whether that's a mutant, like Jean, or combined DNA, like Peter, or gamma radiation, like Bruce. This is how I will be using the term throughout this post, even though normally it would apply specifically to mutants.)
But the more important thought that keeps coming up for me is when Evie tells Peter that his mutating Arachnid DNA is reacting to grief or trauma (and also his loneliness) and how Peter's mutation's sudden surge - and its cause - is a foreshadowing of Jean's mutation doing the same thing at the end of the movie.
Most of the time when we see Jean Grey, it's past that initial trauma point that brought her mutation to life. In the comics, this happened when she was really young: she saw her best friend get hit with a car and mentally connected with her while said best friend died. This is what brought on her telepathy etc.
When we see Jean introduced in BND, it is before this trauma point, although we wouldn't necessarily believe that. We see a Jean whose powers haven't fully awakened. Maybe her powers (and Sara's) initially awakened over the grief/trauma of whatever threw them in the foster system in the first place - we know that their mother abandoned them due to said powers, so maybe whatever happened to their dad caused it. Maybe not - mutations are weird, and we don't know a lot about them or how they'll function in the MCU.
The Jean we see through most of the movie is lonely, the same way as Peter is, but she never considers herself truly alone. Once she finds Sara, she won't be alone anymore.
The Jean we see at the beginning of the movie is angry and desperate and trying to find her sister and is stretching her mutation to its limit to do so. And we can argue that Peter is also stretching his mutation to its limit by being Spider-Man full time for the past four years, with no break, constantly going and going and going.
But Jean hasn't hit that breaking point.
That breaking point is the combined grief of finding out exactly what happened to her sister and how her sister died while going through the trauma of forced, tortuous use of her mutant abilities at a greater speed than even her sister could live through.
And when Jean breaks, her mutation surges. Just like Peter's did. But where Peter fights the surge, Jean accepts it and incorporates it.* Peter's surge in mutation isn't there to hurt him - it's to help him at his breaking point, when he is too overwhelmed by everything and needs the extra surge. It isn't monstrous. It's as much a part of him as everything else is.
I think it's interesting that Bruce hasn't been able to maintain Professor Hulk - that the version of him that Jean specifically brings out is Professor Hulk, which is when Bruce and his monstrous Hulk side cohabit and live in peace with each other - because Jean as a foil to Peter is very much about accepting the whole of your super ability (where Peter's journey is also about accepting the whole of your self - not just the "monstrous" but also a person's dependence on people, which also is not Jean's struggle - Jean knows she depends on her sister and her sister depends on her, that's why she's fighting so hard to find her). And you could argue that Peter sees the risks he causes the people he loves as monstrous - by being Spider-Man and keeping Ned and MJ around, he's being selfish, because they could (and are) hurt - and that's something Jean forces him to confront with MJ. And hiding MJ and distancing himself from Ned are also that trying to fight that monster - but that part of him is also important, that monstrous thing is also who he is, and it isn't monstrous in the slightest.
Sorry - this may be incoherent rambling because the more I think about it, the more it untangles and the bigger the metaphor gets.
*It's also very good foreshadowing of a potential Phoenix Force story - because one could argue that a similar thing happens between Phoenix and the transition to Dark Phoenix, but that's a separate post.