re: re-grading yard / drainage

Probably more extensive depending on how much water you anticipate but you would probably benefit from gutters with those on the back side buried and run to the sides of the house. Then maybe an open french drain up against the concrete patio (existing and new). An open french drain is just perforated pipe buried in fabric and stone but not covering the stone with grass or soil. If you can get enough slope, I'd run it past the new extension and end it with a pop up.

If you have enough slope where it will run to the front from there, then that's all I'd do. If not, you could have a small swale cut in like a shallow ditch on that side between the new extension and fence which will make the water run naturally to the front. I have something similar in my yard that works very well.

Lots of videos on Youtube,,,see French Drain Man or Apple Drains.