There are two files involved here:
(1) Stickies application (Stickies.app) located in the Applications folder. This is part of the MacOS suite and cannot normally be modified are replaced by the user (unless you are reinstalling the MacOS). This is just the app, it does not have actual Stickies content.
(2) Stickies data base. This has all the text and information for your stickies.
I think you really want to restore (2), not (1), from your Time Machine, correct?
The Stickies data base is in user/Library/StickiesDataBase.
Here, user is your username.
One approach: quit Stickies. From the Finder, under the Go menu hold down the option key and you will see Library, select that to go to the user/Library folder. Look in that folder for StickiesDataBase. If you find it, select it and select File => Duplicate. This will make a copy of it, just in case. Then, leaving that file and its duplicate in the window in front of you, go and enter Time Machine. Browse your backups and restore from a backup that has the original (not current version, which apparently you don't want) Stickies content that you want back. It might be an older, maybe much older, Time Machine backup date. Selecting a recent one will probably just restore what you already have.
You can replace the current StickiesDataBase file with the backup that you think has what you want. You have a backup copy of the current one just in case.
Then exit Time Machine and restart Stickies. Are your Stickies back?