You will need to install a user script manager extension to install this script.
Note, March 2021: AO3 changed how it displays kudos, so currently the userscript may not be able to find your kudos if it's further down the list of kudos. However, it should still remember when you click the kudos button in the same browser. Make sure your browser doesn't clear local storage/cookies/cache automatically.
The script automatically checks for kudos you left. To mark a work as seen, use the "Seen ✓"/"Unseen ✗" buttons. (Disclaimer: "Unseen ✗" button doesn't make your brain unsee the thing.) The "Seen works" dropdown menu appears wherever there's a list of works or bookmarks.
Remembers when you bookmark a work. You can page through your bookmarks list once to make it remember the works you bookmarked previously.
If you're logged out the first time you visit AO3 after installing the script, it will ask for your username.
Much ado about buttons: