The add-on transmits one thing: the 11-character YouTube video ID of the
page you are viewing. It is sent over HTTPS to archive.org and
web.archive.org in order to look up an archived record of that video.
Those services' own privacy policies apply to requests they receive.

Nothing else is transmitted. The add-on has no server, collects no
analytics or telemetry, sets and reads no cookies, and attaches no
identifier of any kind to its requests.

The optional browsing-history and bookmark permissions, which are off
unless you turn them on, are used only to search your own machine for the
title of the video you are looking at. Those results are displayed in the
panel and never leave your browser.

Lookup results are cached in the add-on's local storage, keyed by video
ID, for 30 days when a record was found and 6 hours when it was not. This
data stays on your computer. The add-on's options page shows how many
results are cached and lets you delete them at any time.