If this is the first time for you to create a local database to test Identity, you might need to make sure that database has been created. If you didn't do anything to create the database, you might take a look at this section, I mean you might run Update-Database
in Package Manager Console window
Here's my test result, I create a new .net 9 blazor web app auto-rendered mode, and after I run the app the try to register a user, I got error message below, which indicating that I'm not able to connect to the database, but the truth is that I haven't created this database yet. But since we didn't see the inner exception you shared, I'm not sure whether we are facing the same issue.
If you do face the same issue as mine, if you press F5 to continue the app, you might see screenshot below which suggestion you to run update database command.
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Best regards,
Tiny