PeerTube uses the BitTorrent protocol to share bandwidth between users by default to help lower the load on the server, but ultimately leaves you the choice to switch back to regular streaming exclusively from the server of the video. What follows applies only if you want to keep using the P2P mode of PeerTube.
The main threat to your privacy induced by BitTorrent lies in your IP address being stored in the instance's BitTorrent tracker as long as you download or watch the video.
In theory, someone with enough technical skills could create a script that tracks which IP is downloading which video. In practice, this is much more difficult because:
