WTH would I do here? "The tile is significantly higher than the carpet."

I'd buy a Fing Silver Spring wheel chair ramp for doorways from Wayfair.

Notice some are tapered on sides, THAT'S A GOOD THING.

Another case of milling the dimensions you want from lumber stock. Looks like the carpet is medium pile with pad so you would need a butt edge, and maybe restretched straight (?). I believe this is a pocket door so you shouldn't need tapering of the threshold on the end out of picture.

This is so helpful. Thank you!