Start here. This is the direct spoken answer to practice first.
Why this question matters
A completed deployment can still fail at artifact extraction, process startup, configuration resolution, identity, dependency access, migration compatibility, or request handling. Diagnosis starts by locating that boundary before changing the system again.
I would first separate deployment failure from application startup failure. I would check deployment logs, whether the expected artifact reached the slot, App Service runtime version, startup logs, app settings, Key Vault references, and recent database migrations. If the app starts but fails requests, I would move to request logs, dependency failures, and Application Insights traces.