Pine.blog (https://pine.blog/) is a RSS feed reader, a blogging platform and a blog RSS feed directory (https://pine.blog/search).
On the reader part: 1. you have a timeline of posts from the feeds you have subscribed to. The whole look and feed in more like Twitter or Micro.blog. 2. You can have more than one timeline - so this is a bit like folders. The reader is free at least for now.
Blogging Platform: $5 per month. It does support webmentions. Since I don't want to spend money for a blog, thats all I know.
RSS feed directory: This is the exciting part. You can add your blog's feed even if you have an outside blog. Free, but you need to sign up for a free acct. Adding blog feeds to the directory is not real intuitive but not hard to figure out. Human reviewed. Once your blog feed is in the directory it's very easy for any Pine timeline user to add your feed to their reader. But anyone can use this directory to find feeds.
Also for you coders, Pine has an API.
Also, also they have an iOS app.
Followup: I added both my blog and the directory blog to the RSS directory named above and 12 hrs later they are in the listings. I suggest you add your blogs.
ADDED: I just checked the directory search function. It does indeed spider the contents of your feed. Example: For Indieseek blog the term "technorati" only appears in a post. A search for that term turned up the Indieseek blog. Cool.