For myself, I am in the mostly "mundane" camp for martials, because that is what distinguishes them from casters.
Now, as I've mentioned, I am fine with stretching the limits, but with your list it then becomes an issue of "by how much"? I think (or hope at least) for the sake of compromise, most "mundanies" like me would be happy with more, just not
way more.
Increased movement? Double? Triple?
Super jumps? Same...
Physical immunities? The narrative creates a lot of this for myself, anyway. Grew up in the high mountains or arctic, so you have resistance and (maybe) at higher levels immunity to cold? Sounds okay to me. Have immunity to radiant damage? How??? Begins to sound like it is part of an origin story or it becomes too magical for my tastes...
Bypassing immunity or resistance? Though "incredible skill"? Resistance sure, but by the time you get into bypassing immunity it again might be too much...
Break
anything? Really,
anything? Probably not. Toppling a pillar to bring down a roof? Sure. Snapping a magical sword with your bare hands, nope.
Mult-part reactions? No clue, do you have an example???