I'm using this add-on, which does exactly what the name implies: https://addons.mozilla.org/en-US/firefox/addon/mute-sites-by-default/
That gives you a little speaker icon on the tab next to the website name, so you can click that to unmute (or right click on the tab -> unmute), and vice versa to mute it again.
My primary use case was to silence the message notifications from discord and whatsapp web, but it's now really a staple to prevent any unwanted noise.