You can address the areas you'll use for seating by leveling that space in order to place furniture so the seat will be comfortable. Especially if you install some kind of flooring material. If the ground only stays wet for a short time after a rain, you can likely solve the accumulation with a little fill before you install pavers or stone as a patio. Sand is often used. Determining your soil makeup and drainage time will influence your option choice. A couple hours vs a day or two makes a difference.

I would think leveling some spots is a good idea. But not perfectly flat so the water will flow off in the direction you want it to. Have one spot farther away that is lower than the yard for water to collect and create a rain garden with water loving that don't mind wet roots.

This is especially good for drainage from downspouts to be directed. A swale is like a wide shallow ditch that you can mow or you can fill with river rock and have it meander out to the rain garden like a "dry" creekbed.