When switching projection modes, all options in the pop-up sidebar are grayed out.

The greyed-out choices usually mean Windows has temporarily lost the display connection, so it has no second screen available to project to. Since it happens mainly through the dock, the dock, cable, or its display driver is more likely than the Win + P shortcut itself.

When it happens, disconnect the dock from the laptop, power the dock off for a minute, reconnect the monitor cable firmly, then connect the dock again. Check Settings > System > Display to see whether Windows detects the external monitor. Test the monitor connected directly to the laptop as well. If the options work reliably that way, the dock or its connection is the cause.

Install the latest BIOS, graphics driver, and chipset driver from the laptop manufacturer, plus the dock firmware or driver supplied by the dock manufacturer. Do not rely only on Device Manager saying that the driver is current.