Restoring an image to the LR library

If this image has been deleted from disk but not removed from your current Catalog, you can simply use Finder to put a copy back on the current drive. The Catalog's Folders panel will confirm which folder it should go into.

If this image has also been removed from your current Catalog, then there are two ways to put it back. The first way is to import it to your current Catalog once more - copying it into your current working drive as part of this. Depending on whether when you edited it before, those edits were written out to the file - there may be XMP metadata alongside the file describing the image's edits as they were then. If this is a camera Raw then this would have been written to a sidecar XMP file in which case that should be included in what's copied to the new drive. This method will not reinstate any virtual copies, collection membership, some other attributes.

If those last attributes are important to you and exist within an older version of the Catalog then the only way to transfer them is using a Catalog based method - probably (!) overkill for a single image. Briefly, for a set of images you wanted to transfer the full Catalog info for, you would selectively Export as Catalog, then use Import from Catalog to merge these into your main Catalog.

Copy the photo file from the previous HDD, and paste it into the folder where Lightroom Classic expects it to be.

By the way, its not clear to me if you actually have backups of photos and don't have backups of your catalog file. It kind of sounds like just by luck, you still have the old HDD sitting around. Backups, in my opinion, are mandatory, not optional.