Had this issue in another tenant that I pay for and Auth0 had to do something on their side. With this tenant I just have the free version.
The user is logged as being registered but is not showing up on the user section of auth0. Is this normal?
As you mentioned, there was an incident with the search users feature that required some changes on how this feature works and resulted in tenants needing to be mo migrated to the new search cluster. For scale reasons there was different treatment applied to accounts with an active paid subscription, a free subscription with active usage, and a free subscription with no usage. You can read more about this in this incident details.
If you have a tenant in a free subscription and experience issues such as not seeing new users in the Dashboard then it may be the case that the tenant had no detected usage and was not actively migrated to the new user search. In this case, you should contact support through the email address listed in the incident linked above. If you don’t mind disclosing the tenant name publicly then we can also try to sort things out through this public forum.