Your garage is mine's twin. I'm sorry. The big difference between you and me is my garage isn't attached to the house. I got very lucky - I made a friend who is also an electrician, plumber, ex-general contractor, framer, mechanic, etc. I don't think there's much this guy CAN'T do. Couple years ago, he did jack up one side of my garage, pulled out all the rotten wood, replaced the sill plate, sistered the studs, replaced the windows and door, etc. Basically, fixed the garage. Mine was not structurally stable before the work. If you leaned on one corner the whole garage would sway. It's still a POS garage but at least it's functional. In my case, the slab is below grade and is also broken into multiple pieces. Maybe I'll get lucky and my neighbor's tree will fall on it so insurance will pay for a replacement.
Keep digging out around your garage, get the dirt away. If you have a dip, then I've got a post on here from earlier this year trying to figure out what to do about it that might be helpful. That at least will help stop things from getting worse.