Deployment of a new version would depend upon your setup. Assuming a setup similar to the author, you can have a new Docker images with the new version of your code and run it in parallel. All you have to do after that is point the traffic from the old version to the new version (By just running `docker compose`).
If you have a more complex setup, e.g. if by using Kubernetes, you can do things like run both the version at the same time, person A/B testing or have canary deployments to ensure the new version works .
Time for deployment would be most likely in seconds unless the setup is complex/convoluted.
Schema modifications are another beast. For small use cases, you could run a specialized one time container that performs the modifications, but once you need high availability, you'd have to consider a more complex approach. See https://queue.acm.org/detail.cfm?id=3300018