I suppose this is the documentation you were looking for:

The functions erlang:exit/1 and erlang:exit/2 are named similarly but provide very different functionalities. The erlang:exit/1 function should be used when the intent is to stop the current process while erlang:exit/2 should be used when the intent is to send an exit signal to another process. Note also that erlang:exit/1 raises an exception that can be caught while erlang:exit/2 does not cause any exception to be raised.

You are correct. Ask yourself this question: Why try … catch should catch asynchronous event? Do you expect this to catch also?

Process.exit(self(), :timeout)
try
  :timer.sleep(1000)
catch
  :exit, :timeout -> :ok
end

You can; you just need to do Process.flag(:trap_exit, true) and have a handle_info clause to handle the {:EXIT, pid, reason} message that you would receive.

I think you want to look at Process.flag/2 and the meaning of :trap_exit. It still won’t do what you want, as you’ll need to handle it by receiving the message in the process mailbox

Exactly. My point is, to do what you want it to do, the sleep would need to be enhanced to install a clean up callback and raise when something else happened. It is a lot of work for no apparent gain. The Elixir document on sleep is clear that you should not use it: Process — Elixir v1.18.2

Use this function with extreme care. For almost all situations where you would use sleep/1 in Elixir, there is likely a more correct, faster and precise way of achieving the same with message passing