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.

I have vinyl plank with huge dogs in my walk out basement where they have free access to a large dog run it has been in for 11 yrs and still looks awesome. We have a laminate on our main floor that looks like slate and has also stood up to the brats for 11 yrs there is no way wood could have handled all that abuse. IMO laminate or vinyl plank in good condition is better than scratched up wood floor that would have to be refinished before sale. We now have a great pyrenees as our 2 old dogs have passed away and he really is rough on floors , no wood could possibly stand up to him.The pic is the laminate floor and the old dogs

I prefer to stop the tile in the kitchen/nook. The hardwood can then flow from the formal dining area down the steps and into the living space. The ONLY thing that would cause any concerns would be the ability to find MATCHING stair treads for the hardwood you choose. Sometimes this is a BIG problem...if that is the case, then moving the tile all the way into the dining area would be the way around it. But you have to find this out BEFORE you choose/order your flooring. You do NOT want to make this decision on the fly...only to find out that you cannot find more of the tile in the same dye lot...that's WORSE than having miss-matched treads. Much, much worse. All of these decisions/questions MUST be answered WELL before you put pen to paper. A designer who is well connected in the building industry would be able to do all the leg work for you - without much effort. S/He would have already run into these issues DOZENS of times in their career and will know the ins and outs of working around these issues. And s/he will have ALL the needed professionals on speed dial. Which then becomes the NEXT dilemma which MUST BE dealt with before pen is put to paper. Whew! Lots of things to do before anything is decided. A well versed designer can be worth his/her weight in GOLD at this point.

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.