Time Machine doesn’t just do simple documents and such. It does pick up some OS-related elements. For example, Mail and Photos often get updates that make them less than fully compatible with older versions, ergo restoring data files for them could break them. For this reason (and likely others), I would imagine Apple has blocked this backup restoration path.
I’m guessing you can’t even see the files because the OS can’t “adopt” the backup set, and is trying to protect you from manually deploying anything from it that could corrupt your OS and apps. Additionally, Apple may be trying to protect the backup data’s integrity for the system that made it.
You would need to bring the High Sierra machine up to Ventura (if the system will take the upgrade) and then have the upgraded system “adopt” the backup.
Unfortunately, size DOES matter. Is this card over 32GBs in capacity?
https://support.apple.com/guide/disk-utility/file-system-formats-dsku19ed921c/mac