What do the red switches do in Superliminal?

They are fire alarm pull stations. They never actually activate an alarm or do anything else relevant to gameplay, but they relate to a number of achievements. Here are their descriptions as given in Steam:

• Fire Alarmist: Pull one fire alarm
• Expert Fire Alarmist: Pull enough fire alarms
• Fire Safety Achieved: Pull all the fire alarms

If you pull all the alarms (completing the Fire Safety Achieved achievement), then there is another bonus effect:

The main menu screen will have an option with a fire alarm icon, and if you choose it, a sprinkler animation will play in the background. Other achievements and secret-finding can also add features to the main menu scene.

I believe the alarm stations in the “Clone” chapter which do not function normally do not count for the achievement, but I don't have proof.

If you're trying for the achievements, make sure to always turn around when you pass through a doorway to see if there's one on the wall behind you.

Related: the fire extinguishers, often found next to the fire alarm stations, have a set of achievements for emptying them (clicking them until they wheeze) and if you empty all of them,

Clicking any fire extinguisher in-game will cause it to shoot fire instead of white clouds.