accessing stickies stored in a time machine backup from another Mac
My MacBook Pro hard drive crashed (running Monterey). While it was replaced, I borrowed a new MacBook Pro for 2 weeks with a fresh install of Monterey. Before returning it, I made a time machine backup of my latest work to the same drive I'd used previously for my now-broken computer.
(There's very little I need from that latest backup (from the borrowed computer)—mostly just some notes recorded in Stickies. I wish I'd just emailed myself the info, but it didn't occur to me. I thought I'd just browse the backup files and find what I needed. But the username/Library folder appears to be empty on the backup disk (browsing in Finder, there's a "-" sign in a red circle over the folder icon), and when I enter Time Machine on my old (restored) computer, I can see all the backups with dates from both computers, but am unable to enter any of them. (When I click on them, nothing happens).
Is there any hope to recover that little bit of data?
MacBook Pro 15″, macOS 11.2