Hessian Building Code - Garage Border Construction

No, or not without the neighbor's consent, since the heights are always measured relative to the terrain location at the boundary on the building plot, so where your garage is located.

Doesn't the reference height of the neighboring property apply for the height of the vehicle shelter?

If you want to have a building encumbrance registered, you could also have a longer garage registered. Something like "if you want such a high embankment, we want a longer garage." Our building authority once told us that they basically don't care what happens on the boundaries between private properties and that the neighbors just have to agree (within certain limits, of course, and safety must always be ensured), and the building encumbrance just legally secures that.
How does one come up with the idea to allow a 1.5 meter height difference like that?

doesn't the reference height of the neighboring property apply to the height of the vehicle canopy?

No. Always the height of the building plot.

Best regards
Dirk Grafe

No. Always the height of the building plot.

Best regards
Dirk Grafe

and which height on the property? the original height is usually unknown.

Example:
paved area with a substructure 20cm higher than the neighbor's (normal boundary with 40cm high border stones (1 meter long).
on this paved area, a carport with a 3.00m average height carport is installed (measured from the surface of the pavement). from the neighbor's property, the carport is now 3.20m high. this is allowed because you calculate from your own property (paved area), right? the original height is theoretically unknown, especially if you have a slope...

and what height on the property? the original height is usually unknown.

The original height is only unknown if the architect does not do his job.

Example: paved area with substructure 20cm higher than the neighbor (normal border with 40cm high boundary stones (1 meter long). A carport with a 3.00m average height is set up on this paved area (measured from the paved surface). From the neighbor's property, the carport is now 3.20m high. This is allowed because you calculate from your own property (paved area)? The original height is theoretically unknown, especially if there is a slope...

Depends. If no current legal dispute is ongoing or imminent, I will save myself the answer as it is so extensive it exceeds any scope here.

Best regards Dirk Grafe