Two things.

It may be preferrable to keep the stair treads the natural color, and then use a darker stain on any actual trim. Think that all of your horizontal/foot-trafficked surfaces are the same. It seems a little weird, but that is how things were done.

As far as getting the matching stain, what you need to do is take a piece of the sanded wood to be stained and a piece of stained finished trim, and head to Sherwin-Williams. You may have to press them a bit, but they have the ability to adjust their BAC wiping stain to match, but it depends on them having the actual START and END pieces to work with. I have similar colored 'bungalow' woodwork, and I think my base stain was Chestnut with a bunch of extra pigments added.

I agree with Kats. The treads stay light (like the floor but it doesn't have to be a perfect match) and everything else stays dark. It's pretty traditional, and it looks like you have a traditional home with nice old woodwork (and is that chandelier original? too fabulous!).

Also, dark floors (and steps) show dirt.

As a veteran of various stain matching projects, I suggest you make sure to do any cleaning and refinishing of your woodwork. I have a door stained a bit too dark as I had not yet cleaned the other doors when I did the stain matching.