Get why it isn’t in there since it’s unimportant to central narrative, but during Robert’s Rebellion, wouldn’t Edmure Tully be involved by being a squire to a knight?

Depends on Edmure’s age at the time – there’s a pretty wide range for Edmure’s birth date, and it’s quite possible he was only eight years old at the time. Remember, Edmure’s the youngest of the Tully kids.