I had the same problem. Had old strip flooring that was over 100 yrs old. At one point someone replaced a section with 3/4 thick wood floor but you wouldnt know until it was tore up. When I laid all the flooring an got to the the hallway I was up about 1/2 in. I shimmed up an 1/8 in then stripped a blank of the new floor on the table saw to build a thin transition piece. There is a slight raise but everything is the same level and looks nice. So in short just use a reducer.

sorry...moving it over to the flooring forum.

I think having the stairs a different color, especially when you're redoing both the upper and lower levels, would stick out. I would recommend trying to re-stain the stairs to match the darker color floors (be warned that dark wood floors will show everything BTW). However, if you don't want the expense right now then I would save up for it. Not sure if you can re-stain your stairs or if you'll have to replace them, but if you have to replace them buy some extra wood when you redo your flooring for future use so that you don't run into the problem of having no match.

We have hardwood on our main floor and LVP on our stairs down to the basement as well as on the basement floor (over cement). When the LVP was first installed on the stairs (it's been a little over a year now), my husband thought the "lip" part of the stair treads (the bull-nosed edge piece) was not installed perfectly flush and secure on several (I think 4) of the treads, so I wonder if that is not uncommon and is what your flooring contractor is worried about. I didn't even notice it, but my husband is a perfectionist and it bothered him. Rather than complain and have the installers come back to address the issue, my husband fixed the issue himself. I think he used tiny little nails (with no heads) to better secure the edge pieces to the adjoining LVP pieces, and I used dots of acrylic paint from my art supplies to cover the bitty nail holes. We have never had a problem with them since and we are up and down the stairs many times daily so they get heavy use. Just wanted to mention our experience in case that makes any difference for your decision. I don't regret using it on our stairs. We picked an LVP that coordinates pretty well with our upstairs hardwood in color, just a little more rustic which fits our basement vibe. We didn't want to introduce yet another type of flooring just for the stairs.