AFAIK, Piped always proxies the videos through a server.
I am more familiar with Invidious. Find an Invidious server that lets you enable proxying. Some examples are yewtu.be, invidious.protokolla.fi and inv.nadeko.net. Then find an RSS app that lets you download the content, as well as supports cookies. Use the invidious server's cookies in your RSS app to proxy the content you download. Invidious servers can provide RSS feeds for individual channels, as well as your complete subscription feed.
And if possible donate a dollar or two, regularly, to the invidious server that you use, since it takes up a lot of bandwidth and motivates the hoster to keep up what they are doing.