Your iPad Air3 has a Lightning port - which alone cannot provide sufficient power for the SSD.
An iPad with a Lightning port will require that you use an Apple Lightning to USB3 Camera Adapter to connect USB devices to the iPad. This adapter has both a USB 3.0 Type-A connector and an additional Lightning port to supply power, from your Power Adapter, to both the iPad and connected device. The Power Adapter must be rated at 12W or more.
- Lightning to USB 3 Camera Adapter
https://store.apple.com/xc/product/MK0W2ZM/A

To be recognised by iPadOS, the attached USB storage device must be formatted to FAT, FAT32 or exFAT (i.e., FAT64) with a single data partition.
Some additional information about connecting external storage devices to your iPad can be found here:
Connect external devices or servers with Files on iPhone - Apple Support
https://www.imore.com/how-use-external-hard-drives-your-iphone-or-ipad