Site Health: Ensure that the user will be notified after a successful snooze action.

After clicking remind me later, the user is shown an admin notification.

Fixes #48333.

Props desrosj, sathyapulse, Clorith, azaozz, audrasjb, afragen, whyisjake.
 

Built from https://develop.svn.wordpress.org/trunk@48359


git-svn-id: https://core.svn.wordpress.org/trunk@48128 1a063a9b-81f0-0310-95a4-ce76da25c4cd