Are there any requirements or potential issues regarding moving my setup to cloud server?
Is that a matter of creating a backup and restoring it on freshly deployed instance or there is more to it?
On premises setup will still be operational for testing purposes, so no licenses need to be transferred, only configuration of dial plans, extensions, recordings, logs, etc
Yes, there are lots of things to consider. Each cloud server is different. For example, NATs can be a big headache for SIP connections.
That’s probably the minimum to get started testing. Keep an eye on any SIP trunks that are registered eg. running two systems that are registering the same single trunk can cause your inbound numbers to route randomly to the two systems.