I would think that you have to check the Show Library Folder box prior to being in Time Machine. If it shows up in your current view, surely it'll also show up in the backups.
What version of the OS did you upgrade from? If it was pre-Big Sur, you might try the earlier person's suggestion of looking in Users/[your name]/Library/StickiesDatabase. Navigate to that Library folder, enter into Time Machine again, go back a few backups, and see if StickiesDatabase exists.
Yeah, plug in your backup drive, navigate to the folder above, then choose to enter your Time Machine. A machine I have that's on Big Sur shows the same location of stickies, so Ventura wasn't the OS where things got moved — meaning that backups should exist in this location.
When you're in Users/my name, go under the View menu on your menu bar, choose Show View Options, then choose Show Library Folder, which should be toward the bottom.
Try going to /Users/[user]/Library/Containers/Stickies/Data/Library/Stickies. The stickies should be in separate .rtfd files. That's what I'm seeing within Ventura.