ankigate_bridge.ankiaddon.Chrome has no way to see which desktop application is in front of you. The extension needs that, otherwise "study Anki for 30 minutes" could be satisfied by leaving Anki open behind a game. So Anki reports it itself.
The add-on runs a small server on 127.0.0.1:8766 — your own machine only, never reachable from the internet — and answers these questions:
Nothing is uploaded anywhere, and nothing in your collection is ever written to. To answer those four counts it reads your deck list and review log inside Anki, but what crosses to the extension is only the totals themselves — no card identifiers, no note contents, no field text, no question or answer, and no list of which cards were involved. With those goals switched off, none of it is computed or read at all.
If you use the "pick up where the video left off" behaviour, the add-on keeps a small file inside its own folder (user_files/media_pos.json) holding how far through each card's video you got. That file stays on your disk, is pruned after 60 days, and goes when you delete the add-on. The privacy policy sets all of this out in full.
It also registers an ankigate-anki:// link with your user account on Windows, which is what lets the extension start Anki when Anki isn't running. Chrome cannot launch a program; it can open a link. For compatibility with extension versions from before this add-on was renamed, the older focusgate-anki:// link is registered alongside it.
Separate, third-party, and what the extension uses to read your card count.
2055492159, restart Anki.webCorsOriginList contains "*", then restart Anki again.