It would appear that Kroger is being sketchy (why would I ever assume otherwise?) with their SIWA.
You can currently link a Kroger account within the app to a SIWA account.
However, you do not appear to be able to create a new account using SIWA, you must enter in your name, email, and password.. I guess you could still just copy and paste the SIWA private relay email, but a password is still required.
IMO one of the benefits of SIWA is removing the password vector. If an account has email/password access plus SIWA there is now two potential attack vectors, with email/password being the easiest. Although email/password might be fairly secure, one of my goals is not only to be more anomalous but to enhance security of my accounts.