Passing cables through existing walls nearly always involves taking part of the drywall off to gain access to the core of the wall. If you need to feed a wire across an entire wall, you typically have to cut an entire strip of drywall off along the entire length of the wall.
If you have access to the beams beneath the floor or in the ceiling, you may want to do most of the run there, then drill into the desired wall through the sill or header plate. That allows you to get the cable into a specific stud gap to limit the amount of drywall affected.
But unless your house was built with cable pipes/runs built into it (and I can’t imagine this being done outside of commercial buildings), you have lots of futzing around to do, and no small amount of drywall work.
It’s actually drywall on both sides with no firewall but one side is the garage which is not insulated, so there’s insulation on the wall I will be running the cables through, which will be done horizontally