This is weird, I had Zoom installed a long time ago but uninstalled according to their instructions [1]. I'm a macOS user.
As soon as I clicked that link, the client downloaded a PKG file, installed itself and launched itself without asking me if I wanted to share my camera or audio.
I uninstalled according to their instructions again, searched for all "zoom" files in my disk and rebooted.
This leads me to believe that following their uninstall instructions is insufficient, and there are hidden files left on my computer.
Don't be sorry, same thing happened to me just now and I'm trying to figure out how they are installing locally from a URL click with no further input from me.