Putting the url of the site in should usually work. There is a standard called RSS autodiscovery that lets a reader discover the address of a RSS feed without there being a badge on the site etc.
There is an official Chrome extension for RSS:
https://chrome.google.com/webstore/detail/nlbjncdgjeocebhnmk...
I have no idea why it is not part of the default install though.
I feel like RSS has gotten harder to use lately.