Utilize the plot ratio for new construction, build over the terrace

Regarding your terrace, you had a kindred spirit here in December , and building with five children is also not overlooked here:

I am a programmer; when someone comes to me with quite precise ideas about what the program should do, fewer "adjustment loops" are needed

Telling a developer precisely WHAT the program should do is indeed helpful; specifying HOW it should do it is rather fatal. It's the same with architects, who also exist in IT. ;)

Does this also generally apply when connected to the main house?

Garages are and remain outbuildings, floor area ratio II. If you plan something different with the garage (overbuilding with living space), no boundary development can be built.

I am a programmer, when someone comes to me

I assume that every service business is based on good advice. Moreover, the professional should know many options due to his knowledge that the layperson does not know. And I lump crime scene cleaners, programmers, and cooks together here :)

If you have other plans for the garage

No, no, not at all. I just always wanted to have direct access from the garage to the house. Somewhere I had overheard that the garage counts towards the floor area ratio I if it is connected to the house. If that is not the case, all the better!