How do I rotate a physical display showing a virtual screen?
For mirroring, rotate the physical target display in BetterDisplay. For streaming, use the stream's rotation controls. The virtual screen supplies the desktop. The receiving display or stream determines how it appears on the physically rotated panel.
If you are mirroring, open the physical display's App Menu block > Screen Rotation and choose the required angle, such as Rotate Screen by 180°. BetterDisplay can expose rotation for a supported mirror target even when macOS System Settings does not show that option.
If you are streaming, open the virtual source's Stream Virtual Screen menu and use the 90°, 180° or 270° rotation button for that stream. Streaming requires Pro. This rotates the captured presentation rather than changing the physical display's system orientation.
Rotation still depends on the display and connection. Receiving a virtual desktop does not add hardware rotation support. If the option is unavailable on a dock but works on a direct connection, compare the two connection paths.
See Screen Rotation, Streaming, and keeping rotation after wake.