How do I connect my LG Ultrafine 4K 24" display to my iPad Air 5th Gen running iOS 16?

Your iPad Air5 supports DP Alt Mode over USB-C. The Air5 does not support Thunderbolt. Only 2021/2022 or later models of iPad Pro support Thunderbolt3 monitors and connections.

As such, you’ll not be able to connect your iPad to an external monitor using a Thunderbolt connection. For your Air5, you’ll either need to connect to a monitor using a standard USB-C/USB-C data cable, or via a suitable HDMI or VGA Adapter.

• USB-C Digital AV Multiport Adapter

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

• USB-C VGA Multiport Adapter

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

Although the iPad Air (5th generation) has a M1 processor, Apple does not say that it supports Thunderbolt 3. The USB-C port supports "Charging, DisplayPort, [and] USB 3.1 Gen 2 (up to 10 Gb/s)."

iPad Air (5th generation) - Technical Specifications

The only things that suggest possible Thunderbolt support are the M1, and "up to 6K" resolution for the external display. As far as I know, every Mac and iPad Pro that uses the M1 supports Thunderbolt 3. If this iPad Air does not support it, it would be the "odd man out." My impression is also that 5K and 6K display support involves the use of two DisplayPort sessions within one Thunderbolt connection, so "up to 6K" seems to be inconsistent with "no Thunderbolt."

Still, the 24" LG Ultrafine 4K Display takes Thunderbolt 3 input. If the iPad Air (5th Generation) doesn't have TB3 output – just USB-C (DisplayPort) output – that could explain the inability of the iPad to work with this monitor.

I did a quick search on Google and am seeing reviews saying that the iPad Air (5th generation) has a USB-C port, but not Thunderbolt.