Remove the gable roof and construct a hip roof, flat roof, or shed roof

It has already been mentioned: apparently the house is located in a residential area that a) requires a gable roof and b) possibly also red brick cladding.
Therefore, check the development plan carefully!

So if you are emotionally attached to the house (which I can understand), I would quickly abandon the murder plot from Post #1. Would there be anything against visually separating the extension? I find the following example a bit crude, but it can certainly be done nicely.

Possibly also in combination with the looped dormer, or the dormer designed as a protruding cube:


The most important question, however, is: what are you even allowed to do, and is there still enough space on the property (it looks pretty tight in the second picture)?

I find the following example somewhat crude,

... a period should have been placed here because ...

but I'm sure that can be done nicely as well.

... I don't think so. Is this supposed to be an architect's edition of a McMansion Hell?

Possibly also in combination with the @11ant loop dormer,

Whaat ? (+ 30 characters *LOL*)

Painting bricks… the paint will not last long in the joints. I estimate that a new roof covering, new windows, and a thorough facade cleaning can achieve more visually than a coat of paint or plaster.

Painting bricks… the paint won't last long in the joints.

You already said that elsewhere about the same object:

The problem was probably the joints, where the paint simply wouldn't hold permanently.

The @Pinkiponk-style thread splitting seems to be becoming fashionable :-(

Hey, it does not require a new roof. It was a consideration to get a more harmonious appearance. The extension is supposed to be two stories. I have no idea yet how to achieve that harmoniously. Maybe you could make the dormer and the extension look similar, that would already look better!

For the facade, we are seriously considering plastering. Painting over the brickwork COULD also look totally ridiculous, right?

I assume it will definitely look "ridiculous." In the USA, it's common to quickly "spray" facades; for brickwork, I would find that :eek:

If you absolutely want a modern look and the exterior walls of the house are energetically fine, consider the option of a curtain wall facade. Materials like Trespa, wood, glass, aluminum, composite materials, etc. are available in all colors and shapes. A combination of plaster (extension) and curtain wall facade often looks good, too.