Soft disconnection
Soft disconnection removes a display from the active desktop through software while its physical cable can remain attached. This changes which displays participate in the desktop; it is different from dimming an image, turning off a backlight or sending a monitor power-off command.
BetterDisplay provides the operation through connection management where supported. The app checks safety conditions before allowing disconnection, and standby behavior and recovery differ between Apple silicon and Intel Macs.
Read Device header and connection before using it, especially for a built-in display or an Intel Mac. That page explains the safeguards and recovery actions. Display Connections covers the related preferences.