I use and recommend a selfhosted FreshRSS instance, but I’m unsure whether or not it plays nice in terms of accessibility. For finding feeds I mostly just look for RSS on websites that I come across. Another thing I did when moving to FreshRSS was using Feedly, a paid RSS reader with a free plan that I was using, to find some interesting sources and import those into FreshRSS. I also use Reddit RSS feeds for a few subs that don’t have a big enough audience outside of Reddit. Unread articles is no problem for me. I just have a very quick glance and then mark everything as read if there’s too much. After that I check it a few times per day, only check what seems interesting, and mark the rest as read again.