Yes, upgrading to the next version is supported. An upgrade often means migrating the database to a new schema. If done correctly, it won’t affect instances, networks and other resources.
Since each OpenStack deployment is unique, there is not a single upgrade method. You find guidelines in the documentation, for example for Nova: https://docs.openstack.org/nova/pike/... or Cinder: https://docs.openstack.org/cinder/pik....
Moreover, release notes (https://releases.openstack.org/pike/i...) include upgrade sections that warn about pitfalls.
Generally, you have the option to shut down your cloud, upgrade all services in any order and start it up again. This includes suspending your instances and migrating the databases. If your instances need to keep running while you upgrade the compute nodes, you should live-migrate them to a different compute node, upgrade Nova and the hypervisor on the original node, then migrate them back.
If you can't afford the cloud downtime, you need to do a rolling upgrade, one server at a time and one service at a time. Pike- and Ocata-level services are usually interoperable; if not, that should be stated in the release notes.
The internet provides many resources on upgrading an OpenStack cloud. Examples: