I backed up my old Mac on a G-drive. How do I find documents on it when I connect it to my new Mac?

Time Machine is tightly integrated into MacOS so that it can have the access needed to perform backups of everything. Time machine stores the smallest possible amount of additional files possible with each incremental backup, and uses a database it creates with file links to point to older files already on the backup set.

DON'T use Finder on your backup drive. To examine and restore from those backups, you use Time Machine.app (not to be confused with Time machine Preference pane):

Restore items backed up with Time Machine on Mac - Apple Support

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-OR- if you want to bring over most your old documents and settings and passwords from your backup, you can use Migration Assistant running on the new Mac, with the backup drive attached. USB-2 is good enough for this purpose.

Move content to a new Mac - Apple Support

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