Is it safe to install the outdoor unit of an inverter AC indoors?
Think of it this way.  You're transferring heat from the garage air, or from the outdoor air, to the upstairs living space above the garage.
The garage may be warmer than the outdoors when you start the system, but there's far less available heat, and you'll quickly transfer all available upstairs.  Soon the garage will be colder than the outdoors;  you're basically making your garage into a walk in cooler.  Yes, once it's cooler than the outdoors, heat will seep into the garage through the walls and windows and floor, but too slowly.
The practically infinite air outside, although less dense with heat than the air in the garage, contains far more energy.  That's ultimately the source of the heat.