Install a window afterwards?

No, I haven’t posted that yet, I just wanted to know about the window first. :) Since the actual kitchen planning is still in the future.

I would budget a few thousand euros for the new window & plaster inside/outside and hope that we will manage well with that. For the kitchen itself, I’m calculating a max of 15k, so max 20k for the project overall.

Well ... it can't hurt to make the plans now. Maybe good ideas will emerge that can still be planned. And I have seen and considered many kitchen plans where the kitchen owner previously thought there was only this one option, and in the end everything was quite different.

Maybe good ideas will emerge that can then also be planned. And I have already seen and considered many kitchen designs where the kitchen owner had previously thought,

I think so too ;)
When I read the following:

We also wish for more daylight and a nice view of the front yard and garden.

A bit more light"

… I did not think of a fixed element.

I thought of a solution with a fixed lower element.

This option certainly has its justification, however, the struts also take away quite a bit from the window or light.
Therefore, I would first do a brainstorming about what the kitchen with possibly adjacent rooms (dining area?) offers in order to find the best for oneself.

That’s why the concrete description of the stove already puzzled me a lot, as if it was already in the middle of the discussion or execution.

You mean because of the oven? That it should be placed as high as possible is certain for us, if it can be implemented in any way. Whether that will work remains to be seen when we get to the concrete planning. We already have a preferred arrangement, but when it comes to this, we are ultimately laypeople. A kitchen planner will have to see whether all that is possible or if there are better alternatives. But I think it only makes sense to take a closer look at everything when we are a bit further along. First, the budget has to be there... but that has already helped me a lot in assessing effort and costs. :)

.. I would now start planning. There is a good forum ... because possibly there will be constellations that might also influence the financial planning.

I think I know which one you mean :) I've browsed there a few times already. Maybe that would really make sense. I will definitely think about it.