Accessing old Time Machine external hard drive backups after Migration to new iMac

I used Migration Assistant to transfer data from an iMac Monterey OS to the latest iMac Sonoma OS. I have not been able to access my old external Time Machine from either the desktop icon or using the Command/Shift/C method. All I see are a list of numbers and dates on which those numbered backups were created/saved. I don't know how to open/access my old backups because when opening a date, there are three folders, HD, HD - Data and Recovery. Inside the last saved/numbered backup from the Monterey, I opened every folder, each expanded to a degree, the HD - Data has all of the user aliases created. Each iCloud Drive (Archive) has a folder with a red minus sign; empty. There is no way to open any of the old Time Machine backups to restore what I need. I have activated all of the permissions for TM that I know of. The browsing feature is only working for the last week of the new iMac. How do I access the old 2TB external Time Machine that has backups for my MacBook Pro, 2015 iMac (my main backups) and now, my new iMac?

I have backup items from 2019 that I have to save! And I am missing items (movies, music, videos, photos) from the original Migration that never made it so I have to sift through this external hard drive "TM". The "drive structure" method isn't working for me. Is there a simpler way to have access? I can't recycle my old iMac unless I can find a way to easily search and save my backup files. Can anyone help?