Wiring like that requires removing drywall and then patching and then a new Paint job. It will be more like thousands than hundreds. You should take a hard Look at just using wifi extender with an Ethernet port.
If you can’t do that you might see if there is a way to go up the downstairs Wall outside the drywall and do a floor plug upstairs. Could work if you could live with wire mounding or Trim in a corner.
Or do it like an AT&T installer and poke it outside, staple cat 5 to your siding and then poke it back inside once you get upstairs. Not kidding they do sh!t like that.

Note on what you’re looking for and why it will be so hard. Your house wall has a top plate. A 2x4 on its side. Then there is floor decking. Probably 3/4” plywood. And then there is a bottom plate on the walls up there. So your electrician has to drill a hole thru 4” of solid wood to make a whole from 1st to 2nd floor. You need a big drill for that. There is no way to do that without removing some drywall.

Good luck with the project. I’d pursue wireless options. You can easily bridge the floors and still have ports.