The overlap time setting is located in the service's Settings pane (not project settings) under "Deployment Teardown." If you're unable to find it there, you can alternatively set the RAILWAY_DEPLOYMENT_OVERLAP_SECONDS service variable or use config as code with the overlapSeconds field in your railway.json or railway.toml. Note that overlap time starts counting once the new deployment becomes active, so setting it to 120 (seconds) would keep the old deployment alive for 2 minutes after the new one is ready, which should cover the gap you're experiencing.

It has not been resolved; I have tried adding the RAILWAY_DEPLOYMENT_OVERLAP_SECONDS variable but I have not observed any change in behavior in my service.

Your service has a volume attached (mounted at /files), and Railway does not allow multiple deployments to be active simultaneously on services with volumes, to prevent data corruption. This means the overlap time setting has no effect on this service regardless of how it's configured. Some downtime during redeploys is expected when a volume is present. If zero-downtime deploys are critical, you would need to move the volume-dependent storage to a separate service (e.g., an object store) so this service can run without an attached volume.