Building a coop for 6 chickens
You are at max having 6 in your coop. The run is suitable to hold about 3. Of course you can keep the 6 in what you have , but overcrowding causes all sort of problems. If you could increase run size or let them free range, then things would be more ideal. This is calculated for 6 standard chickens.. If you were to have bantams, then the acomodations would be more fitting. The guide not rule. is 4 square feet in coop and 10 square feet in run per chicken.
WISHING YOU BEST
Remember when designing the run are that there will be times that one is under the coop and must be fetched out. ie: broody and not in a good place to be, sick or injured and needs help.
Drop down or removable sides on the lower part helps a lot.
Your sketch looks like it could work. I personally like having a run I can walk into and no access under the coop for them. I do not enjoy crawling under to get a chicken. (been there done that)
If you can go bigger that is always better when it comes to chickens.
For a visual for you I am including a pic of one of my old coops that was 4x6 and had the 2 foot tall under space. It may give you ideas for yours..... or not.
I built it inside the existing run which was very difficult.
Inside the coop.
Space saving idea. This was mounted to the clean out door.