the sharing system used for this video implies that some technical information about your system (such as a public IP address) can be sent to other peers.
The threats to privacy with YouTube are different from PeerTube's. In YouTube's case, the platform gathers a huge amount of your personal information (not only your IP) to analyze them and track you. Moreover, YouTube is owned by Google/Alphabet, a company that tracks you across many websites (via AdSense or Google Analytics).
The video quota only takes into account the size of <x id="START_TAG_STRONG" ctype="x-strong" equiv-text="<strong>"/>uploaded<x id="CLOSE_TAG_STRONG" ctype="x-strong" equiv-text="</strong>"/> videos, not transcoded files or user export archives (which may contain video files).