You want to start with a chemical stripper. Methylene Chloride is the most common, fastest working, strongest, and unfortunately, most noxious. Put it on and let it work. Do a few steps at a time. If you have nice weather, open the windows for a breeze. The biggest problem people have is not giving it enough time and then having to spend more time and effort on a second, third, fourth ... application. Scrape off with a putty knife and follow up with a scotch-brite stripping pad. Neutralize / rinse as directed on the can of stripper. Then let the wood dry thoroughly. This will remove the polyurethane and generally most of the stain. Oak, having coarse pores in the spring-wood, might retain some of the stain in these rings. Don't kill yourself trying to get it out, just leave it as a contrast. Often people think they can just "sand off" the finish and avoid the chemicals. Bad idea. After a whole weekend and a pile of gummed up sandpaper, and only part way through the project, they think it's a bad idea, too. The other risks are that the finish is removed unevenly (causing the subsequent stain to absorb unevenly) and if there is veneer (not likely on your steps, but highly likely on casegoods), it's easy to sand through. An exception to this guideline is if you are doing a hardwood floor with a drum sander and removing significant amounts of wood with 36 grit belts. Once dry, do a light sanding with a fine sandpaper (120-220). I think you might want a stain, something like a "golden oak" if for no other reason than to even out the tones in the various pieces of wood. If you want to preview what the unstained wood with varnish only would look like, simply wipe some areas with a rag dampened with mineral spirits. I would also recommend applying a good floor-quality polyurethane. This is one instance where you need the abrasion resistance of a poly. Get a good brand, not just a can of polyurethane at the grocery store. Just because it says "Great for Floors" on the front of the cans mean that it's the best choice. If you want, you can thin it 50-50 with mineral spirits, creating your own "wiping varnish" and wipe it on. You will need 2-3 times as many coats as a brushed on finish, but it's fairly foolproof as a DIY or beginner. I also like to sand between coats to smooth it all out, remove imperfections and dust nibs. If you are wiping on, every other coat should be OK. If you are brushing, be sure to thin it so it flows out better.

I have done this. We have oak railings in this house that were very ho-hum, so I decided to stain them darker with polyshades. I mixed Walnut & Bombay Mahogany & while I would have liked them to be a bit darker brown & less reddish, I'm very happy with the way they turned out. My railings did not have a really shiny finish, so I didn't sand or anything, just painted right over them with the Polyshades. I used a small cheap chipbrush, so I could just throw them away, since Polyshades is oil-based & I hate working with oil. It covered really well in one coat & I just went back & did a quick 2nd coat on areas that were a bit too light. I didn't even tape off the spindles or anything & it was quite easy to control the coverage. Here's a before & after..the best pics I have available right now. Now the railings are much darker than the floor & I think it looks much better & richer. And it really wasn't hard to do at all. Well worth the effort. Before: After:

Have you reached out to the installer? Seems like it would be their responsibility to fix this-

I am wrestling something similar except I have hard wood I am staining and adding new to hall way. I feel like I need to use golden oak (my guy uses duraseal). But I was thinking of going a little more brown. Please let us know what you decide. I might check out nutmeg for my red oak flooring. Suggestions...I will let you know what it ends up or me