First floor plan – please provide criticism/tips

I already understand that. You are planning a garage in the north so that you can get into the garden with the trailer. We suggest leaving out the garage in the north, and you say then you will make an entrance there... You are planning an entrance there anyway, so what would be different without or with a garage? Then I would consider how often you need to get into the garden with a trailer and why. I find paving for a trailer (maybe once a year) exaggerated. Whether the entrance in the north is sensibly placed anyway, with or without a garage, we cannot judge. For us, the option is the east, which should be doable with any common layout for a city villa.

What I generally wonder is, is it allowed to build the garage to the street right on the property boundary?

Primarily, there are setback areas according to Art. 6 Bavarian Building Code that must be observed. In designated building zones, there is the so-called development plan. Here, the development boundary to be observed for the property is explicitly indicated.
If one exists, then the questions are already answered within it.
(You can find it in/on (Internet/ municipality/ building authority/....))

There are also exceptions, such as garages/ outbuildings, usually with a floor area of up to 20 m², which may also be built outside the development boundary and on the property boundary. However, they should maintain a distance of 3 m to public streets.

However, you should measure a 3 m distance from public streets.

I have to correct myself, or rather further define the definition of distance to the street. The distance is still 3 meters. However, for public traffic, green, and water areas, I am allowed to already include half of the (in this case) street width (street + sidewalk).

Specifically, this means that if the street is 6 m wide, I may, if nothing else is noted in the aforementioned local development plan, build directly on the boundary.

Conclusion: If a development plan exists, then read it!

Yes, a development plan is available. It clearly states that the distance between the building envelope and the street to the east must be 7 meters. However, since the garages do not have to be built within the building envelope, in my opinion, we are not bound to the 7 meters. Otherwise, I cannot find any information in the development plan – so the rule from BauRoman would probably apply.

Since the plot to the east along the street is about two-thirds higher than the street (and the height difference is compensated with boulders), it cannot be built completely up to the boundary anyway. I have now sketched this with a double garage – and moved the house up to 3 meters towards the northern boundary, as the single garage is no longer there. The garage is slightly set back to the rear so that a kind of "embankment" is created towards the street to the east. The yard is currently probably still somewhat oversized, but as mentioned before, we want to be able to maneuver relatively easily on the property.

At the same time, I have also considered shortening the house by one meter on the short side (to then 8.5 meters) – to gain more distance from the neighboring building to the south (whose house is about 3.5 meters from our boundary).