I am 99% certain that is rift sawn white oak. I can tell it is rift sawn as opposed to quarter sawn because I don’t see any of the “rays” that are typically present in a quarter sawn oak. I believe it’s white oak because the yellowness indicates such where as red oak is more white but with red/pinkish grain hence the name. There are testing kits that use wood shavings to test exactly what species of wood grain it is.

We’ve had our fair share of white oak floor repairs and one thing I will say is that because of the age of the treads, getting an exact match, colorwise, won’t be possible because of the difference between old growth and new growth and the aging your treads were subject to. For the most part the difference in color should be subtle but could be noticeable.

If you do go ahead and refinish these steps, you could test the color matching by getting a sample quarter sawn plank, put a coat of poly on it, then sand a spot on the steps (ideally where the finished has mostly worn off so it’s easy to sand), coat with poly and compare the colors. If the color is close enough and doesn’t bother your then go ahead and replace the tread. If it stands out and bothers you(which I totally understand), I’d maybe consider doing a glue and epoxy repair if the split in the tread is clean enough for you to get a tight and sturdy fit with glue.

I do see what you mean with the top tread. Looking at the wear on the lower stairs it looks like there was a was a runner on the steps and it must’ve been glued down at the top. Lucky for you, a good sanding with 40 or 50 grit will clean those steps up real nice and the color of all of them should be consistent.