What Google Tag Manager sets, and what this site doesn't.
None. The archive dropdown menu and share buttons on each archive page run on plain JavaScript with no cookies or local storage involved.
Archive pages load Google Tag Manager (GTM), which may in turn load Google Analytics to measure aggregate traffic. That can set cookies such as _ga and _gid in your browser, used to distinguish visitors and sessions โ not to identify you personally.
The site shown inside the iframe on an archive page is a separate, independently hosted page and may set its own cookies under its own domain โ this policy only covers the frame site itself. See the Disclaimer.
You can block or delete cookies in your browser's settings at any time. See Opt-Out Preferences for a more direct way to disable Google Analytics specifically.