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I searched for "mute" on both but on yours I only find sets but not specific mute icons?

You have to click the top-left Search icon to do a sitewide search.

That's confusing, especially on the main page. Why not have a single search that includes multiple types of results, kind of like Spotify?

Beats me. But I do agree with you, I felt the same way. I just wanted to point out that the feature does exist.