Are the electrician's holes in my framing a structural concern?
That's all fairly typical, and I don't see anything concerning. The electrician could've kept things a bit cleaner by either going easier with the auger bit or notching the stud cleanly instead. They're in a hurry, like everyone else, though.
The holes in the wall plates only remove a minor portion of the width of the plate (which appears to be 2x6). It does carry one floor joist, but that could as well be carried by a 2x4 wall, so it's fine. I would pilot and install a screw to secure that split plate shard just to prevent a bulge in the drywall. Be sure to not pinch the cables. They must remain free to move.
If a repair was deemed necessary for some reason not evident here, a short double-2x6 header behind the wires with trimmer studs to the bottom plate would do.
The large hole in the flatwise stud doesn't really matter because that stud isn't critical to begin with.
I would consider replacing the nails in the protective steel plate with flathead screws, countersunk to be flush. That'll help with what might otherwise be a visible bulge in your drywall. Even nails with smaller heads would help. You could use trim nails and drive them flush. They just need to keep the plate from sliding around before the drywall goes up.