Ooph m15o to the rescue
Your actually looking for 3 things! A desktop feed reader, a mobile feed reader and a feed aggregator (the thing that collects your feeds and syncs them)
Its true, most feed aggregators are paid these days and while you can self host FreshRSS (Like meeeee) it only makes sense economically if you already have your own web server.
If you use a Mac and an iPhone you can use
NetNewsWire and it will sync your feeds over iCloud for free, but thats only good if you are into the Apple ecosystem.
Im surprised more e-mail providers don't also offer feed aggregation