There won't be any "wear" since the tire is not moving.
I don't believe that you need to move. It is considered OK to let cars sit in one place for months, so why not trailers?
In the "old days" , car tires used to get flat spots if allowed to sit for some time. When you started driving, the flat spots would thump for a few miles, until the tire warmed up and rounded itself out again. For more, check out
https://www.continental-tires.com/ca.../flat-spotting
or any number of other sites that come up when you do a search on "tire flat spotting".
On the other hand, I have always felt that if you are going to sit in one spot for some time, you would do well to set the tire on an untreated wooden board or plastic mat. I believe that blacktop, concrete, or bare dirt, can absorb some of the oils from the rubber. For example, check out
https://www.rvtravel.com/why-use-syn...es-on-asphalt/
or other sites.
Bill