Recommendations for a deck roof

I’m building a new deck for my parents (in Pacific NW).

This is the house and the yard and you can see the deck pilings. The deck will run the full length of the back section of the house 24’ and extend 10’ out into the yard. It is literally just under the french doors in height so no railings or steps needed. Composite decking if anyone is curious.

The request is to put a small roof over the door to keep a dry patch by the back door, but not too much to block any of the “sunlight”.
My question is— how should I build the roof? WHat do you all think looks good?
The options are:

  1. A small roof that extends out (slopes toward the picture taker) from the wall above the door and the windows (~11 ft. wide and ~3 ft. outward).
  2. The same outslope roof the entire length of the deck.
  3. A peaked roof (A-frame just above the door and window)
  4. “Extend” the existing roof out 3 feet.

For options 1 & 2. Do you think I should run posts at the corners? Would a simple (minimal framing and a single layer of shingles) 3’ roof out be able to be supported by just wall studs?

For options 3&4, I figure I need to match the slope of the roof already there, but should I drop it down about a foot or so below the existing roof?