The idea would be that you could move in the depth axis just as an fps player (or maybe arcady spaceship or aircraft game?) moves through all 3 dimensions.

Though honestly I don't play many 2d platformers, what I've seen is more of a ... reset or rewind kind of paradigm, or jump forward in time, fastforward, or pause.

I'm thinking of some kind of... like you'd have to solve certain environment puzzles, defeat certain enemies, by deftly and precisely navigating through time as much as deftly executing platform jumps and 2d combat.

EDIT:

Like maybe imagine this with either a DPad + Stick or Twin Stick setup.

The one of those is your normal 2d movement, the other has one axis that is time forward/backward.

Or, maybe, left right is side to side, your character is some kind of unable to jump or crouch, but instead time phases with up/down?

(jump and crouch are replaced by... gravity temporarily off, gravity temporarily x 4?)

Pair it with maybe some kind of time travel stamina/mana meter, you gain more 'endursnce' with experience or after getting a treasure or accomplishing some task.

Could I guess also work with a top down or 2.5 uh, perspective as well, I guess?