Could you get unfinished wood flooring (same species and width) and have it stained to match what you already have?? That would seem to be your best option.

Of course, you would have to decide what to do about the carpet on the stairs then.

Easy to match the wood - install unfinished flooring and have it stained to match. You might have to have old AND new stained/re-stained so it all matches perfectly. We did it in our house and you'd never know some was original and some was added later.

Definitely site-finished hardwood to match existing. It's messy and disruptive, but if done properly will last for decades.

What they said. Yes it’s a messy and expensive project (I had many square feet of site-finished hardwood installed at my last house) but worth it. And particularly so for your house.

Yes, you can match your current hardwod. I would not add dark tile. If you recarpet, use a lighter blond/taupe/greige carpet that works better with your wood than the current gray.