Sand down the area first to knock the raised edges around the hole away as that is part of what makes it so visible.

Fill in the hole completely. Caulk, sheetrock compound (spackle is basically the same), or wood filler putty will all work. Once dried sand it smooth and fill in again if needed.

Let dry for 24 hours before painting and if you still see a dark area where the hole was after the paint dries for a couple hours add another coat. You may still see the touched up area however if the walls are dirty, the paint has been worn, someone had smoked in the room, the walls are exposed to direct sunlight, along other things. If that is the case wipe down the area around the repair and see if that will help. If not plan to repaint the wall if it is too much of an issue.

Honestly the best thing to do is not put holes in the wall to begin with or do so sparingly and reuse those holes for other stuff.

And in this day and age we all know wireless exists and that wired is ALWAYS a better option than wireless for speed and stability. There is no point in mentioning it.

Wired>wireless every day of the year.

They make something exactly for this and using staples is called a cable tacker. Doesn't pinch the cable at all and is great for temporary or long term use.

Go grab a cable tacker. Then just run it wherever you want and it will stay out of the way.