1st off you will have quite a height difference between the tile & LVP floors. Unsure why LVP in a non wet area. It will also be much colder and no sound deadening like you get from the carpet. If you want a hard surface floor I would suggest Cork in similar color tone as tile. It will be a warm & quiet floor. Take a look @ Wicanders brand.

I hate wall to wall carpet anywhere and I do not think bedrooms need to have the same flooring as the rest of the house . depending on the type of LVP there might be very little difference at floor level. I have laminate in my bedrooms it looks like cararra marble it is only in my bedrooms.My only concern is getting a vinyl that works with that tile since the bathroom has that same tile