What you said is right, but I basically said the same thing.
I'm one of Piped's main developers...
I don't get the question. How's that related to Mozhi?
Mozhi basically acts as a middleman between you and the translation api, it doesn't store any user data.
Piped/Invidious proxy everything through YouTube, except for any kinds of user data, as that data is stored on the server you use.
Mozhi is proxied through the server/instance you use.
I've been talking about the case that you're logged in with a Piped account, which makes your subscriptions and playlists become stored at Piped's server.
Piped does more than just proxying at its backend, the only thing that you could really call to become proxied are thumbnails and video playback.