@Huma0 Yeah, gotta love it when the contractors claim "oh, that wasn't included in the quote". Unfortunately, you have to get everything nailed down in writing prior, no matter what a great rapport you feel you have with your contractor.
I was lucky in that my boyfriend at the time was a carpenter, so he helped me renovate a lot of the house. As I recall (it was 30 years ago) we just used a side grinder with a sandpaper wheel attachment for the treads and I sealed it myself. The hardwood floors of course required a big sander rental- they weren't painted, thank goodness, just worn, stained, and had old yellowed varnish in the non-traffic areas. And I always used a water based sealer with no toxic fumes, several coats.
But ouch, 3 flights of those beautiful wide stairs of yours! That would be quite an undertaking, not to mention create a huge mess for quite awhile. I think if it were my place, I'd consider just sanding any really rough spots by hand, then painting them. That way it could be a work in progress and not too disruptive- just do a few stairs per weekend. Hopefully you'd live long enough to get to the top 🙂
It's curious- way back when, everything was just the natural wood. Then around the 40's, apparently the way you showed that you weren't poor was that you painted all the wood (See, we can afford paint!) Then in the 80's-90's everyone was stripping all the paint off to get back to the natural wood. Then around the new millenium, I saw a trend in the house mags to be painting all the wood again, mostly white.
I never try to keep up with any trends, just do what is appealing to me.