How can I blank one display without changing the desktop layout?

Keep the display connected and use software dimming or a supported screen-control command. Disconnecting it removes its desktop space and can move windows or change which display is main.

To darken the image, use software dimming on the intended display. A black image does not guarantee that an LCD backlight turns off or that the monitor enters standby.

For a hardware screen action, open Settings > Displays > [display] > Additional Settings… > Display Connections and set Display menu on/off switch behavior to Screen Control, if a compatible controller is available. The display’s App Menu switch can then darken the screen while retaining the connection. The switch requires a controller that supplies the relevant screen state.

DDC screen control depends on the monitor: some models do not support it reliably or cannot wake again through the same command. Keep a working screen and a manual recovery method available when testing it. DDC Power Off is a separate action that requires manual power-on. It is not a substitute for a reliable screen toggle. See the display header and connection switch for the choices and confirmations.

If you want a fully dimmed image restored after sleep, review full-dimming restoration. Keeping the desktop connected does not guarantee that macOS and the monitor preserve the dark state through wake.