First, do what you need to get the car under control.

Then, switch on the hazards so the driver behind you gets a heads up. Obviously you don’t risk crashing fumbling for the hazards.

Particularly useful on rural roads with many turns where the slowdown really might be surprising, or on off ramps where the car behind you might not have arrived yet.

Usually there is a buffer where you've noticed a hazard in front and are braking in time. But then your next focus is on what is behind you. Did they notice you braking hard, are the about to hit into you, do you need to move over for them, etc. Hazards just add a bit more warning that red brake lights, because they're so common, can't convey.

It's done afterwards, once you've safely reduced the speed of your vehicle, not during the initial emergency braking.

It's basically a heads up for all the vehicles far behind you that haven't yet noticed a sudden change in the flow of the traffic. Gives them more time to reduce speed without haste.