My favorite has to be Gladion's battle theme, he was not only my favorite character, his theme was the only one that I bother listening to while I play USUM everything else I turn off and play my own music as background music.
The song that plays during your video call with Professor Kukui at the beginning. That song is so amazing and instantly pulled me into the game when I started up Sun for the first time. I wish they used the song more.
The E4 theme is amazing, glad I don't have to link to it since it's already in the first post. ='p So catchy and I listen to it probably at least once every couple of days. ♡ I'm also really into the trainer battle theme! very catchy!! oh, and and oh my goddd so amazing, especially knowing this is our theme song as the first Alolan champion