How do I connect an external SSD to my iPhone SE 2022?

Sure, but not for backups. This if the Related Article linked above is relevant to your goal.

Here is how to: Connect external storage devices to iPhone - Apple Support

You will need to provide sufficient power for the SSD, whether via the Lightning to USB 3 Camera Adapter, or via an external power supply intended for the SSD. I’d expect the external connection will work better. Whether the chosen adapter can provide enough power?

Manual file copies will work, as will as shortcuts.

iPhone backups are to iCloud, or to a Mac or PC.

You can also connect to a local SMB server on a Mac or Windows system, and copy individual files that way.

No, but the Sandisk iXpand thumb drive plugs into the Lightning port and has a management app.