Backups in lightroom

The backup of a catalog will contain all of the editing record of what was done to those raw images. However, it will not contain the raw images. If you can associate that catalog with the raw images in the same folder they were previously contained in then it would be possible to export JPEG copies containing all of those edits. And, if that catalog is the catalog you are synchronizing with the cloud, you would be able to create collections and synchronize those images with the cloud.

Of course, this is assuming you are using Lightroom Classic.

It would really help if you told us if you are using Lightroom (Lr icon) or Lightroom Classic (LrC icon); and also tell us the version number.

Assuming you are talking about Lightroom Classic:

Basically is it possible to restore backups on a new system if old system suddenly stops working?

Yes

What i mean is that i had edited a number of raw pics on the old system but neither did i export to the cloud or export those raw files to jpeg.

Exporting or saving in the cloud is not needed, and not necessary.

Will copying and pasting lets say the backup folder resolve this issue?

Sure if you do it correctly. See: https://www.lightroomqueen.com/restore-backups/