An app on Lovable's built-in backend keeps its database on Lovable's cloud. Export it, load it into a Supabase project of your own, and your users keep their passwords.
What you see
Your Supabase project isn't in your own Supabase dashboard, because Lovable created it on Lovable Cloud.
Why it happens
Lovable doesn't move a project to your own backend in one step: the data has to be exported and restored, and storage files, secrets and sign-in settings set up again.
How to fix it
In Lovable: More → Database → Manage → Settings → Export data, then Export on the Database card. Download it from More → Storage when Lovable emails you, with any files your app keeps there.
Create a Supabase project of your own (Launchpad's wizard does it when you turn on Database with Supabase) and deploy.
Load the export: launchpad db restore <the export file> .…