The unlink button you see in the portal indicates that the subscription is linked to you as a partner. Having a subscription linked to you allows you to manage the key. That said, DO NOT unlink the key.
To migrate the system, all you need to do is take a backup of your existing configuration and redeploy to your preferred environment. The steps would look something like this:
1. Take a full backup from your existing system.
2. Stop the existing machine. (preferrably shut it down instead of deleting it for now)
3. Access your 3CX Account and locate the corresponding subscription
4. Press Install and select your preferred deployment method.
5. Upload your backup when prompted and complete the installation wizard.
6. Verify the configuration is restored successfully and completely delete your old VM.
Note: Your Public IP will change so do make sure your SIP Trunk on the SIP Provider end is aware of the new IP if this is a requirement.