What would be the ruling with Sato and the team rules? Would one of your teammate's squads being at distance 1 of a ship allow you to trigger Sato? Or would it have to be your own?

This kinda stems from the whole Dodonna issue and debate and I wasn't sure what wording/ruling would be.

I doubt it would cross over. Like how you can't target a "friendly" aka ally ship/squad to be benefit of a reroll from Toryn or Jan's Brace.

What would be the ruling with Sato and the team rules? Would one of your teammate's squads being at distance 1 of a ship allow you to trigger Sato? Or would it have to be your own?

This kinda stems from the whole Dodonna issue and debate and I wasn't sure what wording/ruling would be.

The only reason Dodonna works on everything is because his effect does not affect his own ships but his opponents' ships. In a team game, both of his opponents are still his opponents, so it works on everything. Sato is a friendly effect, so it would only work on the Sato player's models.