Reddit Random Post reads the URL of the active tab only when you click
the toolbar button, solely to extract the subreddit name. It then makes
an unauthenticated GET request to Reddit's public post-listing endpoint
(https://www.reddit.com/r/<subreddit>/top.json) to pick a random post.

No personal data, credentials, cookies, or browsing history are
collected, stored, or transmitted by this extension. No accounts,
logins, analytics, or third-party trackers are used. The only external
service contacted is reddit.com, subject to Reddit's own privacy
policy (https://www.reddit.com/policies/privacy-policy).