I'm curious about breath holding and freediving: When you're depriving your body of oxygen for such a long time, do you not risk cells dying, in particular in your brain?

If not, how do we know it's not happening?

It does happen-- which is why we're told to watch out for high CO2 levels in our living spaces and let fresh air in often

A slight increase in inspired CO2 levels might cause some mild symptoms but it won't kill brain cells.