This is cool! I definitely think it could be something. The interactions with the doors and the cart were maybe the most interesting part. I think that kind of context switch while staying in first person is something you could build around but might be hard to make lots of bespoke interactables like those. The mantle is also pretty smooth and makes the parkour stuff a lot more managable than in most FPS games. Makes it feel more like problem solving. I like the information that the mantle indicator thing gives you but I might try to find a different visual for it.
It reminds me a little bit of this first-person physics prototype I made a while ago. I was trying to make quite granular controls and my idea was that with granular controls you could potentially make a lot of fun physics puzzles quickly. Things like packing luggage into the back of a car or stacking a bunch of stuff on top of each other. The trade-off for the granularity is that the controls would be a bit cumbersome and it would take a long time but that makes those simple puzzles a bit more meaty. What I ended up with was a lot harder to control than I intended and I gave up on making it better and just made this one level where you have to get a couch out of an apartment and down some stairs. (right and left mouse button are right hand/left hand when the prompts are on screen) https://torfi.itch.io/i-need-to-take-the-green-couch-downstairs?secret=9k8i4Uw5V...
But the context switch with the door controls and the cart kind of reminded me of what I was originally trying to achieve. It feels like you have quite granular control so you could potentially make the player do some really fiddly task.