For eight people and some spillover, you probably need a patio in at least the 350 or 400 s.f. range in order to accommodate dining, lounging and the outdoor kitchen without it seeming cramped. The S.F. will depend on the actual furnishings, amenities and the degree of spaciousness required. A larger, more spacious patio will seem more luxurious than one that is cramped or tight. A little extra space can accommodate extra people should there be occasional parties or such.

You will be linking driveway access to house and pool. In order to accommodate all features needed, a patio might span the full width between pool and far side of house. Then a paved walk might link that block to the drive. (We don't know the scale of the plan so can't measure anything.)

You'd want to decide early on whether the patio will abut the house or if it will be set a few feet from it, in order to allow for foundation plantings which could make the patio seem like a friendlier, prettier, more hospitable place. Plants are outdoor decor and they take room. If you want foundation planting between house and patio I would not make the bed less than 6' deep. You'll want to decide if some shade will come from a small tree (not too close to the pool) or if it will come solely from built structures. If any of the shade will come from covering that is attached to the house roor, you'll need to decide that up front and determine how that covering could interface with the roof. It would simplify matters if a roofed structure was not attached to the house.

You will also want to consider how a pergola or similar shade structure for the patio will affect the indoor light levels and views.

Don’t forget that you need an area of perhaps 3’ (that distance around a table is likely avaialble somewhere but I don’t know what it is) so chairs can be pushed back to let folks out, and you need to be able to walk around the table when folks are seated at it. So it currently looks too tight. That is why upthread I suggested a “skirt” around your table mock-up that would include the distance needed for chairs to move so folks can get in and out. The table also blocks access to one door and perhaps the driveway. So I would move everything outward, including the patio edge, the kitchen and the table, to give enough space not just for the furniture, but also for its use and access to all parts of the patio. If you don’t want a larger patio, consider whether you need a table that large. Would a table with leaves that can open up work for when you have guests or a second table that is usually folded up and stored?

I like the area along the right fence for plantings but would pave the area along the pool because you don’t want to block sight lines to the pool from the patio for safety reasons. You can have really large pots for plantings along the house wall since the windows and doors make beds there difficult. So leave space for those.

I would try to simplify the overall shape and avoid crowding table and cooking area. As mentioned, it looks pinched on space. Also, access to the drive is nearly blocked off.

To be sure, all the bugs aren't worked out but this iteration may help in getting yours to evolve. I'm considering some planting space between house and patio.