I just did the exact thing last fall as when we moved in with my mom, we needed an extra bedroom, my son has his "teenager cave" now. I know it's probably not to code, but I had to do what I had to do.
I had almost exact same issues as you, house was about 3 steps higher, low ceiling if I raised it, no heat, etc. I guess I never updated my home project thread with the build. I will try to find my pictures, but I am at work at the moment, most all are on my home PC.
If you do use most of garage, I would still leave some footage as open garage by big door mayeb with an exit door in the room and garage door button by it. My old neighbor did this, he left about 4' of space, he hangs all his yard hand tools on the wall and has exit door. They did not so a subfloor and that floor gets really cold in the winter.
My situation was a 24x24 garge with pre-existing mudroom and a side door. I also needed to keep some garage so we only used some of garage. I also wanted to move washer/dryer upstairs so I extended mudroom over 8 feet and then added bedroom. My son has to go through laundry room, but he doesn't care.
Oh found a couple pics. sorry for blurry pics, my old phone was about done.
I will try to upload some more this evening if I get a few mins.
Here is a pic with paint work of kind of my original idea of extended laundrry room, ceiling is only 7' in there so we have to deal with that in that little room. I am the tallest at 5'6" so we are good haha.
I built the room 9x14 with a 5x5 closet also. I had to tear out all of old drywall and redo everything. The concrete floor was pretty level, but I used treated 2x4's to lift floor some and insulated between each one and laid plastic barrier over that before adding laminate on top. I added some piping for the heat, but it's so far away from furace, even with a booster fan, we get very little heat, you can see vent in stair riser. not having a return doesn't help either. Mom had an extra Eden pure so we added that, but in very cold winter temps it was hard to keep 62-65*. My son joked it was like he was camping. I had 2-6" layers of insulation above, walls insulated and plastic over then, but I still have to drywall outside of walls and there is missing drywall on ceilings in garage, those would probably help. To do over, I would have spent the money and added some type of floor heating or maybe electric baseboard or would have went with 6 or 8" subfloor and added more insulation.
Here is only a couple pics I have of drywall work. I had to box in the garage door opener on the outside wall.
Steps going out of room up into laundry room into mudroom/hall.
standing in closet looking into room.
Looking into room from laundry
Here is the sliding barn door I made to close off laundry room. It's a collage, but you can see we had folding doors for original hall closet so I made it a slider. We have that door and I made a swinging barn door for my son's room.