I would go with the runner idea. Refinishing is not going to a one day project. I have a runner. I did try without one years ago but found kids slipping on them in footed pj's was a worry. A lot on here say leave stairs bare bit they don't live in your home.

If you want a one day project you want carpet. I wouldn’t do her grey with your warm floors though..

Paint the treads and risers the white of your wood work...high gloss maybe? Match your runner to the wall paint. Simple but lovely.

Refinish every other step please. You'll get a good thigh workout for a few days.

Whatare the floors at the bottom of the stairs those stairs look finished in the first pic so explain a bit more.

Thank you all for your input! I’m attaching a picture of the floors and an up close picture of the stairs (ignore the gate-I have two little ones). The stairs had carpet on them for 30 years so the part underneath looks bad