Terrace roof on trapezoidal plot

I know. The question is whether the 3m distance to the boundary must also be maintained if no building application/building notification has to be submitted because they are subordinate parts.

In Bavaria, it is mandatory. You need the neighbor's consent. If you do not have it: do not build or if already built: dismantle.

I think no one would come up with the idea to ask the neighbors

This "no one" is the OP. And we are in Bavaria. And do not have nice neighbors.

I just checked again for Saxony. Up to 30m² and less than 3m deep is exempt from approval, but only if the neighbors have agreed (and thus the setback distances are observed). So forget my explanations about that.

I don't think I would cover the entire house side with such a component. Honestly, I am still missing the brilliant idea, because besides sun protection, it also seems important to me to be able to leave the house there with dry feet to get to the terrace. The seating area could also be planned in front of the house wall anyway, so that you have a clear (furniture-free) view from the dining room to the outside. In the old house, we had a glass roof, which we liked very much, also because you could sit under it when it was raining; we had already arranged shading with an awning beforehand. Awning alone or sails also make sense, but in your situation, in my opinion, the necessary dry path outside is missing; otherwise, for example, only the area of the wall could have been covered. We have it reversed on the side and like the fact that it is shady underneath during the summer. You have more than enough light, as far as I can see. You would have to see the entire view to say something about it, but I could also imagine building a somewhat narrower (possibly 5m wide) glass roof in the middle, because it is also quite nice if the entire terrace is not covered. Then you could think about something with planting/design of the terrace area, so that it results in a nice overall picture. If possible, I would rather go for 4m depth; that would be more important to me than using the entire width. We originally wanted that too, but then shortened the area of the wooden terrace to a little more than 1m depth and only built the seating area deep and comfortable. Accordingly, you could also consider covering a short piece in the dining room area and going to 4m in the living room wall area; in front of the dining room, design something nice with plants that you like to look at. You might also not necessarily want to have your coffee chat close to the neighbor's boundary. In front of the dining room, if you want it or need it, you can always situationally use a parasol or similar, but in any case, you have dry feet when leaving the house there. So much for my rough idea.

The slanted side is no problem. Glass can also be cut at an angle. Patio roofs may be constructed or altered in Bavaria without a building permit procedure if their area is not larger than 30 m2 and their depth does not exceed 3 m. The construction of larger roofs, on the other hand, generally requires a building permit.

Dry feet out of the house. We don't have that; instead, I have bad weather-appropriate shoes & clothing as well as umbrellas when it pours cats and dogs - which is certainly possible in Ticino at any time of the year. But mostly it only rains lightly - any coat that can handle the walk from the parking lot to shopping can handle that. Honestly, I don't know where the panic about a little water from the sky comes from.

Quite simply, we are always in socks or barefoot inside the house. For the quick trip to the composter, trash bins, herb bed, or garden, there is a pair of "Latschen" for everyone by the terrace door. However, I prefer not to have the chaos of shoes lying around in the living room, so they stay by the door. Even if you have weatherproof shoes (clogs or similar), they are always wet in the rain if you don’t have a roof. We had no roof for the first 2-3 years, but I wouldn’t want to be without it anymore.