I may be the last person to figure this out, but in case I'm not:

My Mastodon browser tab started making an irregular, infrequent beeping sound a few weeks ago, despite my having turned off notification sounds literally years ago.

Turns out the latest Mastodon version (which added quoting) also added a new category of notification sounds that's ON BY DEFAULT when you're quoted.

There's a switch to disable it in the settings on the notifications tab.

You're welcome.