First: It's a beta.
Second: It's not even a public beta, it's a developer beta. It's entirely possible that they just haven't re-implimented it in Safari yet. In fact, it's highly likely that is the case. In the next build it will magically re-appear. Then in the build after that it'll be gone again. That's the way developer betas work.
Third: There are plenty of RSS Reader options that will work with iOS and macOS—though most are now web-based options such as
Feedly. Off the top of my head there is
NetNewsWire for iOS, macOS and tvOS (costs $28 for it all), and
NewsExplorer for iOS and macOS ($10 I believe). Free apps are hard to come by any more. As Vegsvisur mentioned above, most have been abandoned because there's simply no real market for them.
Fourth: Adding via ShareSheet is the tough part... not many options there. Although if I recall, Feedly offers a share sheet feature.
Once Google killed their RSS Reader service, Twitter & Facebook pretty much replaced RSS for most people.