Older home where the living room is lower than the rest of the home, as shown in pictures. There is a slope to the left and right of the patio. This has created a drainage issue. Wife and I would like to do something with the backyard. We’d like to extend the concrete patio to the left and right of where it is now. How would you address the drainage issue? Aka, how would the concrete work on the right side of the current patio?

Ignore the siding condition, plan to address it soon.