Stage manager - desktop view not working: only mirrors, not extends

Begin by updating your iPad to the current version of iPadOS - as some versions of iPadOS 17 have a known bug that affects Stage manager. At the time of writing, iPadOS 16.7.1 is current; with this version installed, it is not mandatory for Keyboard and Mouse/Trackpad to be connected prior to connecting an external monitor.

Be aware that your monitor’s screen resolution will impact the available settings and external screen capabilities. 

While undocumented, testing has demonstrated that 4:3 monitors with a display resolution of 1280x1024 and below are currently only usable with iPad screen mirroring; as such, associated settings to disable screen mirroring in favour of Stage Manager are not available in iPad Display settings.

When used with a 16:9 widescreen monitor, with a native display resolution of 1920x1080 or greater, the full set of Display settings - and access to Stage Manager - become available. Other screen aspect-ratios may be problematic.

The iPad User Guide lists the upper resolution limit as 6K - but the Guide offers no lower limit, or suggestion of aspect-ratio, being a factor for compatibility:

Connect iPad to a display with a cable - Apple Support

This discussion thread may be of additional interest:

iPad Extended Desktop not working - Apple Community

In conclusion, your monitor must be capable of 16:9 widescreen 1920x1080 (FHD) to support iPadOS16 Stage Manager extended desktop. Unless the monitor meets the minimum required specifications, you will not see the full range of controls in iPad settings.  

When mirroring your iPad display to an external monitor, expect to see black bars to infill where the iPad screen doesn’t match the aspect ratio of monitor screen.