Registering a building obligation for a garage - advantages / disadvantages?

Could it perhaps be a bit more specific?

No. Maybe 500, rather 1000, maybe even 5000. It depends on many things. See above.

Dependent on what? You only write can, could, no indications of the set or paragraphs, of the state building code or statutes. Unfortunately absolutely not helpful

I am neither a lawyer, nor an architect, nor an official at the building authority.

I only know that the additional costs for a building encumbrance from our neighbor ended up being around 2,000 euros. This only included the costs for the planner and the approval authority.

If the neighbor only agrees when you first have to slip him 10 purple bills because of the restrictions on the property, then it quickly becomes 5,000 euros.

So: how should I know?

It's not worth the time here. Just 20 cm shorter and the topic is more than settled if the garage is then privileged.

First, I would talk to the architect about which building servitude [Baulast] needs to be registered and why. Normally, you are allowed to build up to 9m along the property boundary if the wall height does not exceed 2.5 meters. This varies from state to state and, as you correctly write, is regulated in the LaBo. However, local regulations can override the LaBo, where stricter (or additional) limits apply. For example, if your development plan provides for a maximum boundary construction of 5 m, you need approval from the building authority (city or [LRA]) for the construction. Neighbors must also always sign the building application there.

There is another house attached. Which is connected to the garage.