Here is an aerial photo.
That is already helpful. Even better would also be a cadastral excerpt.
Bay windows are not much cheaper than enlarging the whole bay depth of the house
I have now understood that it is probably more sensible to plan the house a bit larger than to have an additional bay window.
Correct objection, wrong conclusion. But explaining it in a way that a self-planning layperson would understand would go too far here:
It would really make sense to have someone plan who has studied this for years and has been working in the profession ever since.
Definitely, especially in the 34-series area, you should not do the planning yourselves but go to an architect!
There is no development plan, so we are free in the planning. We simply prefer a hip roof. But I can also understand that a gable roof offers more usable area.
You can do an architecture wish concert if money is no object. Hip instead of gable already costs so much that you could get a "bay window" for it; for both "bay window" AND hip you could already get a garage (with gold trim on the gate). Whoever can still say "yes" at this point certainly has my first-class Swabian envy.
We haven't yet decided on a construction method (solid or prefab house). Would designs from an architect be independent of the construction method? Or does this have to be planned from the start?
The decision about the construction method is wisely left by the builder to the result of the decision-making during the resting phase. See also "A house building roadmap, also for you: the phase model of the HOAI!" It makes sense to plan it from the start—but not from the very beginning during the preliminary draft, rather only at the beginning of the design phase.
Plan the house with an architect (without quotation marks!—i.e., a freelance architect) up to the preliminary draft ("Module A" of my house building roadmap), and then carry out the decision-making during the resting phase before transitioning to the design planning. In this, you ask a handful of house providers ("prefab" and "solid") for orientation offers based on the preliminary draft and, at the same time, for catalog houses that most closely resemble the preliminary draft.
Note: a family with three children practically excludes the possibility of adopting a catalog house unchanged!
A freelance building consultant (e.g., the architect or one of my not so few colleagues) will then advise on adapting the catalog design (often by "extending a catalog base model in the wheelbase"—explained in the post "Changing a floor plan in size").
At the end of the resting phase, one then decides whether the architect should refine the preliminary draft into a solid (stone) design or wooden design, or alternatively whether a catalog design should be adapted.