Took me two attempts to add to my iPhone. On both attempts (the second being successful), I had selected to add to both iPhone and Apple Watch, but it never appeared on Watch.
I went into the Watch app (under Wallet/Apple Pay) and saw an option to add my Digital ID (from iPhone) to my Apple Watch. It didn’t need to scan my passport again, but it required more face scan verification. I’ve tried that 3 times now, and it keeps telling me that I need to complete the verification again
Maybe Apple Watch support isn’t quite ready? Everything running the latest (non-beta) OS