In the Start menu (you know, the fruit button at the top-left corner), I clicked shutdown. I did not unplug the USB-C power cable. The red light was still on, but I thought it was like the sleep light of a PC monitor. After leaving Pi in this state for more than one hour, I just picked it up thinking that it would be cold, but no, it was still warm. I touched the CPU and it was quite warm.
To make sure that it was not on (headless set-up, nothing was connected, not even Ethernet), I tried SSH and VNC. Both failed to connect, so I guess it was in the soft-off state.
But why is it warm? It has no battery, so it cannot be the heat from charging. All devices I have used did not generate heat when they are off, even if the power cable has been connected. So, I cannot understand. Why is it warm after more than 1 hour after being shut down? Does it do something even when it has been shutdown?