Here's one more pic showing garage entrance and ceiling outlet for stairs.

Copy that! You may be able to keep what you have in place, but I would certainly make sure it has dimmer control so you're not over-bright in laundry.

One additional idea for this laundry space would be undercabinet lighting (so simple now with LED strips or pucks) that's also dimmable. That might give you more targeted task lighting while working out a stain or soaking items in your utility sink without needing to reach for the overhead light.

Alternatively, it could be helpful to consider moving the switched box location from overhead to the far wall (rt side, from in front of laundry units) that could help provide a beam angle into the laundry units over-shoulder for sorting and transfer, since there's less wall surface behind from that perspective that isn't shared with the hall area.

In tall, narrow stair halls like this, I often recommend a plan of wall lamps that uplight the tall vault and bounce the light down into the pedestrian area versus directional beams down from overhead. When placed at the right elevation over and above personal height, they don't have to interfere with traffic clearances even in a super-tight space. Hope that helps, cheers!

Dimmer switch! Great idea (I feel stupid for not thinking of the obvious). :-)

Your idea for the stairs is a good one but I just finished painting all the walls and I don't want to open them up & do all that wiring etc. There's also a ledge on the right side that would hinder that idea. The under cabinet lights was also considered but the light there now lights up everything and the new appliances won't have pedestals but a countertop over them making the ceiling light more functional.

Would putting another track light over the stairs be too much?

It may be overkill to do another track fixture over stairs, but you can certainly have more control over it from wherever that stair j-box is with a 3-way dimmer. Easy first option to try it that way and live with it for a time. Then you'll know if you want to move forward and keep iterating or if it's meeting your needs.

I'm going to move that track lighting over the stairs to see how it lights up things. If it works do you think that two of those track lights in this smallish area would look good from an aesthetic point of view?

The track light will be more "blinding" on that stairwell. Just put in a wafer-style "recessed" light. If you can fish in another line put 2 one more toward the landing at the bottom. As to the track, please look at the box, and make sure you get the right dimmer, otherwise, you will get a lot of buzzing noise.