To find the catalogfolderin the copy of the old drive, do a search for a file named "catalog.pse12db". It is in the catalog folder. You can copy and paste the whole catalog folder elsewhere on your new computer, so that even in case of system restore the backup file is safe.
Could you confirm if your backup was made from the organizer as explained by Akash Sharma?
The WaldoData folder is used to index your media files for 'visual' similarity. It is automatically rebuilt if missing by analyzing again all your files (may take several hours).
So, a possible solution would be to locate your old catalog folder (menu Help >> System Information), create a copy of that folder anywhere and delete the WaldoData subfolder before backing up again. However, that implies that you are able to access the old computer. You mention the 'catalog.pse12db' file which is not included in a regular backup from the organiser. Such a backup folder includes a renamed copy named 'catalog.buc', hence my question about which kind of backup you did perform.