I also use dawn dish soap twice a year on the roof and touch up any seals that need it.
The argument I’ve heard against using dawn is that it will take the wax off of your trailer. I’m not convinced that the incidental contact would remove wax. Most of the water coming off of the roof goes into the rain gutters not down the sides. I always wash and wax the trailer the same time I wash the roof anyways.
I don’t have any good recommendation for the awning.
My roof is Alpha Systems TPO and they specifically mention Dawn dish soap to wash the roof.
Here is the Alpha Systems website
And here is a video about roof maintenance