First I assume you are using Lightroom Classic, not Lightroom. Can you confirm that? With either application the edits are stored in the application database, not with the photos. If you are using Classic and delete the photos from your local drive after editing, you can simply correct the link to the missing photos by pointing to the new location on the server. You won't lose the edits because they are in the catalog. Your workflow isn't clear though so I am not sure why you are losing the edits, or even why you are working like this to begin with.