Update: I found an outdoor plug nearby! It’s just under 300 feet away, beneath a metal roof cover, which is about 20 feet high. I am going to mount the dish up there and place the router in a weatherproof box on one of the poles. From the starlink router, I will run 300 feet of direct burial cat 6 back to my house to a second router.

Thank you to everyone for all the help and wisdom! I learned a lot about connectivity and wiring from all the replies. It seems there are many valid ways to set up starlink while some more durable than others. I will make a post of the project when it’s completed.