Why does a display I disconnected come back after sleep?

macOS can reconnect displays after sleep to restore access to the desktop. Enable Disconnect reconnected displays upon wake if you want BetterDisplay to disconnect previously app-disconnected screens again after waking.

Open Settings > Displays > Overview > Display Connections > Connection Management Settings… and enable that option. It is off by default and requires Pro connection management. BetterDisplay applies it after the wake delay, so the screen can briefly return before being disconnected again. The post-wake main display is excluded from this action.

Changing a monitor’s input to another computer does not necessarily remove its desktop from the Mac. Soft-disconnecting it removes that desktop. The wake preference helps maintain that choice across sleep. Neither action guarantees that the monitor enters standby, which depends on the display and connection.

Keep Auto-connect all displays when no connected displays left enabled and Allow disconnecting all connected displays off for ordinary local use. The last-screen recovery rule is separate from your preference to keep a particular display disconnected. If the built-in screen stays dark after undocking, see reconnecting the built-in display before changing those safeguards.

See Display Connections for the recovery rules, or disconnecting a display with a Shortcut for an explicit manual action.