For travel soccer (and I think for most House/Rec soccer as well) they do it all by birth year, not grade.
As for the “u” designation, I think it starts with whatever age the kids are at the start of the fall season. So, for example, the kids who were born in 2013 were all “under 9” at the start of the fall 2021 season, so the 2013 team is called “U9”.
When you register they should sort it out for you simply by asking what year your child was born in.