copying the files from one SSD to the other (so both contain the same files)
By @JanetteFPl
Yes and specifically, they should be copied in a way that the entire folder hierarchy, from parent folder to all subfolders, is copied exactly as the source/original is. This is so when you re-associate the Lightroom Classic catalog with the replacement location, everything can be found the same way. So this is simplest if the current folders are all under a single parent folder, or at least as few top-level folders as possible.
…and then, within LrC, synchronising the parent folder on the new SSD with the copied images would definitely not work ?
By @JanetteFPl
Correct, and it’s smart of you to ask that because a lot of people trip up on this. Synchronize Folder is definitely not what to use in this situation where you want to replace existing files with their backup. Synchronize Folder is for updating the catalog with changes to the selected folder (such as added or deleted files) in its original location. But when you’re re-associating a catalog with a replacement set of identical files (such as on the external backup), tracking added/deleted images is not the goal, the goal is to maintain everything as it is but now linking to the backup files that should be identical to the originals. The Update Folder Location command is what serves that goal.