I was looking into this a few days ago, but was having a hard time finding an RSS reader that was desktop software and handled Youtube feeds. I couldn’t find anything that wasn’t tied to a SaaS or required hosting online.
If you're on iOS or MacOS I can highly recommend NetNewsWire (https://netnewswire.com/).
What readers have you tried? What do you mean by "handled YouTube feeds". YouTube feeds just work as far as I am aware, they are fairly regular feeds. Are you expecting something in particular?
Thunderbird handles youtube feeds just fine.
I believe yarr fills all your requirements. Can run as standalone on linux, and if you click "read here" the video gets embed. Assuming an extra click is not disqualifying. Note I have not verified this because I host it on a VPS.
https://github.com/nkanaev/yarr