Relinking My Collection on new computer without backup/restore

Hi, I've recently swapped to a new computer, and with all the things that needed updating, I forgot to do the backup from within my HomePort, so that I could restore My Collection on my new laptop. I've since wiped the old computer, but I do have old Time Machine backups of it. Is there a way for me to restore My Collection from those old backups? I've done a search for alldata.gdb, but not sure if that's a PC name for the file?

Grateful for any thoughts!