"browsing activity" is the video url/id. And detecting that you navigated to the next video.
If you read carefully you'll see that this only applies to YouTube and RYD API - not all websites.

Nothing in the extension changed - it’s open-source, so you can verify that yourself. What changed is how Mozilla labels privacy-related permissions.

The extension can only access two websites - YouTube and RYD's own website

The extension only uses an anonymous, randomly generated ID, and the id of the video that you liked/disliked.

• YouTube access - needed to read the current video ID and show its dislike count.
• RYD API access - needed for API requests and diagnostics.
• Online/activity data - viewing, liking, or disliking videos. - only on YouTube
• Personally identifiable information - RYD’s random private user ID used to count votes, not your real identity.
• Website content - mainly the video ID.

The new labels sound scary, but they describe the same data the extension has always used.