ipad vertical monitor

The iPad User Guide provides details of connecting external external displays to an iPad:

Connect iPad to a display with a cable - Apple Support

If your iPad has a Lightning port, you will require an Apple Lightning to Digital AV Adapter along with a suitable HDMI cable - or a Lightning to VGA Adapter for older monitors that only have a corresponding analogue video input.

• Lightning Digital AV Adapter

https://store.apple.com/uk/xc/product/MD826ZM/A

• Lightning to VGA Adapter

https://store.apple.com/uk/xc/product/MD825ZM/A

If instead your iPad has a USB-C port, the equivalent Adapters for HDMI and VGA:

• USB-C Digital AV Multiport Adapter

https://store.apple.com/uk/xc/product/MUF82ZM/A

• USB-C VGA Multiport Adapter

https://store.apple.com/uk/xc/product/MJ1L2ZM/A

If you have a 2021 or later model of iPad Pro, for compatible monitors that support DisplayPort over USB-C or Thunderbolt3, you can also make a direct connection using an appropriate cable.

In addition to basic Screen Mirroring to a connected monitor or TV, iPadOS 16.2 also the new Stage Manager feature is available for these models of iPad:

• iPad Air (5th generation)
• iPad Pro 11-inch (all generations)
• iPad Pro 12.9-inch (3rd generation and later)

More information here:

https://www.imore.com/how-use-stage-manager-ipad

Move, resize, and organize windows with Stage Manager on iPad - Apple Support

Feature availability is usually limited by system hardware - CPU and available RAM being critical to some advanced functionality. Models supporting Stage Manager have an M2, M1 or A12X CPU (upon which the M-series CPUs are reportedly based) - with at least 8GB RAM.

Your monitor’s screen aspect ratio/resolution will impact the available settings and external screen capabilities.  iPad specifications and documentation do not mention support for anything other than monitors utilising “standard” landscape orientation. As such, support for vertical monitors might only be confirmed by trial and error.

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.

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.