Build a self-contained EF Core migration bundle in GitHub Actions, apply it to Azure SQL as a dedicated deploy step, then ship the API to App Service - schema and code moving together, with a smoke test at the end.
Calling Database.Migrate() on startup is the demo answer, not the production one. How to actually ship schema changes - idempotent SQL scripts, migration bundles, a least-privilege migration login, and reviewing what EF generated.