The depth of the roof is rather limited by the budget, since we are officially in snow load zone 3 and thus more than 3m rafter span would become absurdly expensive and bulky (according to everyone we talked to).
So we have 4m depth here and that actually wasn't more expensive, but we are in zone 2, as far as I can see. Over here, they used rather narrow but tall rafters. I would find it a bit too much if that covered the entire side of the house, because then you wouldn’t see any of the house at all. Where and how which posts stand (or have to stand) could be drawn out or visualized somehow. If you post the plan as a whole, which is always useful anyway, one can also imagine something like that better. Actually, I would look at that very closely with others or set it up exactly like that for myself, whether it is really comfortable enough, because I would rather not build a lazy compromise and instead help myself with other means (high-quality umbrellas, sails, or similar). Please check this very individually for yourselves, other people have different sensitivities and also tend to present their own way as the best option. I also find it nice if not the entire terrace is roofed so that you also have a part under the open sky. At our old house, we had a terrace across the entire width of the house, the one in front of the living room glass facade had 28 sqm (7x4). We never sat on it even once, but always only on the smaller one. However, in my opinion, this was a bit tight with 3m for several people; it worked, but behind the chair was immediately the end of the terrace. Maybe you have some pictures or details.