No pressure washer, and not a strong rinse, just flood the panels with water so the runoff will take some dirt with it.
Car wash soap is much better than dishwashing soap. It is designed to clean dirt from cars, not food From ceramic dishes.
For a nice paint job you don’t want to scuff or scratch. After a water rinse I like to use a hose end sprayer with the car wash soap inside. Now rinse it off and let the soap sit on it a few minutes, then rinse. Do this twice. This will get off more dirt and grit before you start rubbing the dirt into the paint with the wash mitt. Don’t press hard just move the soap around and rinse.
Now wash it normally. You should never press very hard, let the soap clean the car not scrubbing.
If it’s not good paint then you can’t hurt it, scrub the hell out of it!
dish soap,will strip wax and polish from the paint which can be good start if you are going to wax it again.