Recently, during the past month, we've begun hearing a loud buzzing noise from upstairs neighbor. Seemingly when they're toilet gets flushed or water is otherwise used. Tonight it's been going straight for awhile (perhpas a long shower?) and wondering what this could be...

You really should go ask them and know for sure and save yourself the speculation and assumptions, rumors or gossip. Do you know your neighbor? Do you have a building super to ask?

Maybe a audio recording you can post would surely narrow things down, because it could be anything.

I agree with Talaniman, to check with your neighbor, it may be a minor problem and they are not aware of it, it could be a toilet fill valve an angle valve or any other issue, good luck.

John

Kind of agree with John. It may be kinked toilet supply line, partially closed angle stop, or debris inside toilet fill valve - all may become quite audible when compromised

Milo