The Watchpoint Pack is treated like a new purchase on whichever store you buy from, whether it's Xbox, PlayStation, Nintendo eShop or Battle.net.
If you've bought the pack, you should have immediate access when you launch the game. Make sure you're signed into the same Battle.net account - and that it's linked to the relevant console account you're intending to play on.
If you've already played Overwatch 2 before purchasing the Watchpoint Pack, the Overwatch 2 contents will be added to your account retroactively.