This happens with fire sprinklers a lot, one sprinkler goes off, and triggers the rest of the floor, or sometimes even building.

That’s not how it works. Each sprinkler has it’s own trigger mechanism, the glass bulb, and cannot trigger another sprinkler.

There are systems where this happens, but the sprinkler heads look very different, and you won’t find them in an office building.

Isn’t the water in sprinkler systems a stagnant mess too?

Yes. A combination of rust, thread cutting oil, and water that has been in the pipes often since the system was filled. It smells, it will stain anything it touches, and it’s a smell that’s difficult to remove.

Not true everywhere. Many buildings, especially industrial, require a flush of the fire suppression system annually or biannually to test that everything is still functional.