I paid for the PC version of X-Box Game Pass, linked my account, and noticed I didn’t have my skins, even after waiting 3 hours, restarting Battle net multiple times.
Long story short, “which seems obvious now in some ways” I launched Overwatch 2 through game pass instead of the battle net launcher like I usually do, and i got my stuff instantly.
You’d think Blizzard & Microsoft would have streamlined the process to not require that and just somehow flag your account, but it seemingly does.