Shoe molding will clean that right up.

They are pretty tiny I think I would try Dap which is a paintable caulking first before adding what IMO is bulky trim. The painters should have done that.

I agree with GN Builders, a nice 3/8" x 1/2" Ogee Shoe Moulding will finish that off perfect.

Stairs are constantly in movement...Dap will not hold, it will create more of a mess.

what can I do to fill in these gaps between the stairs/sideboards and each stair tread?

I would rather have the gap than this

or this

And you sure don't want this (quarter round that is often confused with shoe molding)

It would look better matching the tread.

am I the only one who thinks these gaps are small enough for caulk? mask first so you don't get it on the wood treads, and paint over it when done. you'll have to pull up the masking tape before the caulk dries, and then mask again for paint. don't cheap out, and look for a caulk with good stretch. I heard good things about Big Stretch: https://www.lowes.com/pd/Big-Stretch-10-5-fl-oz-White-Paintable-Latex-Caulk/4411173

Caulking should work fine. Follow the instructions in the above post.