They will not be, I would go through the update process on your current host first before doing the backup restore. The main reason for that is the device session keys got moved from redis to postgresql in 4.7 and there is a command you have to run to move them after the update: [release] ChirpStack v4.7.
I believe you could do it the other way around (backup / restore and then run the migration command on your new server) but less likely to run into issues to update your current server, run the migration command, and then backup / restore if you can do that.