Help me with expanding my garage

Move the stairs.

Seriously, if you like the idea, it would be far easier and less expensive to build a catwalk and bump the stairway upward or install a spiral staircase off the corner.

ETA: still need to assure the slab can take the weight of a car...

Put the stairs where???

Either extend out from porch doorway straight out (bridge) then stairway down. Or a spiral off that outer corner.

Any conc. slab built to basic construction standards (4" thick, wire reinforcement, on 4" gravel) is fine for autos.

The lack of insulation and or vapor barrier is not critical in a garage. Condensation is the cause of most wet slabs (warm moist air over a cool slab).

You best bet is a shed structure under the deck that does not touch any of the existing structures. This simple structure could easily exceed your $7k number. As soon as you want to attach to the existing deck structure or the house, there will be another set of rules to play by. The supporting posts for the deck/roof structure are undersized. The building department may want them brought up to current code. When you start touching that, then they may say the whole structure does not meet current code. Decks age and fasteners rust out. Decks fall down all the time because of corroded fasteners. The 30k estimate above could easily be exceeded.

Building a larger shed somewhere would be a better idea. Some companies do not deliver them pre built. They bring them in with pre assembled walls. So the shed can be hand carried to a tough to access spot.

If you don't need a lot of climate control make it into another screened porch. Put metal roofing on the underside of the upper deck to help control dust and blowing rain, a 4' knee wall around all 3 sides and screen up above. You can then make removable panels to cover the screen for a little climate con tool with a space heater or window A/C.

When you ga to sell, just remove the panels and you are left with another screen porch for the kids to play in while the adults play upstairs.

Move the stairs to the left side of the 1st picture going down along the edge of the slab and you can then park a car underneath the deck. Put a man door going from the garage to the slab under the deck and you are good to go.
You can go so far as putting in brick planters around the edges of the slab and some lattice in place to screen it in. Have a walkway out each side.
And if needs be, put a decorative sign up pointing to where the front door of the house is.

Man, sorry to drag this out, I just don't see where I'm supposed to land the stairs in your idea. The landing is nearly to the small shed, which I would rather not lose. Do you mean to double the stairs back away from the shed around the front of the deck?

Luckily, there is already a man door between the garage to the slab!

I'd agree that it's:
Not critical in an unheated garage built on dry ground with no run off issues. All bets are off on wet ground.

Sorry SR1, I am horrible with descriptions and explanations. Move the stairs to the same side as the exterior wall (but at the edge of the deck, not the structure [front side]) and have it run the length of the slab. No need to move the shed.