Terrace roofing - Kitchen too dark?

Hello!

We would like a fixed terrace roof so that part of the terrace is protected from wind and weather.
We do not like glass and we do not want to do any plastering either.
With our current design, however, we wonder whether the room behind it might become too dark, since the roof would have a depth of 3m. On top of that, there is the corridor between the window and the kitchen of about 150cm.

Floor plan. The proposed roof is indicated by the terrace table and the pillar. All windows are floor-to-ceiling (exception: living room behind the sofa)


Here is a visualization via Sketchup. Shadow from February 1st, 2:30 pm. The buildings visible in the aerial photo have been demolished.

Personally, it would be too dark for me - the shading is quite significant if you don't use a glass roof.

February 1, 2:30 PM: in winter it is just before sunset, approximately southwest. Therefore, the sun is low. In summer, the sun is blocked from around 11 AM until evening by chance. The porch blocks the evening sun anyway. For me, that would be too little sun in the house, but something like that is also a matter of taste..,