A new App Service release caused errors after swap. How do you decide whether to roll back or roll forward?

In production I would make rollback a designed capability, not a panic button. Database changes would use expand-and-contract steps, message contracts would stay backward compatible, and releases would have telemetry that tells me which path is least risky. During an incident I would preserve evidence, name an owner for the decision, communicate user impact, and keep compensating data fixes separate from code rollback. The best answer recognizes that deployment state, data state, and user impact can move at different speeds.