FreshRSS is a self-hosted RSS feed aggregator, only downside is the language chosen to build it isn’t with security & privacy in mind.
https://github.com/FreshRSS/FreshRSS
FeedMe as a client reader application for the RSS service, again same issue.
https://github.com/seazon/FeedMe
But hey it’s open source & with no deliberate backdoor programmed, none that’s obvious anyways.