Your iPhone13 lacks a USB Host Controller with which to connect directly to USB/SSD devices. To connect USB storage, you must use an Apple Lightning to USB 3 Camera Adapter:
https://store.apple.com/xc/product/MX5J3ZM/A

Don't be fooled by the name of this adapter - as this adapter adds the USB Host Controller and Root Hub components that are necessary to connect USB devices to your iPhone.
This Adapter has both a USB Type-A port and Lightning pass-through power connection to which you will need to connect a Power Adapter rated at 12W or greater, this being required to provide sufficient power for the connected USB storage. In most cases, your iPhone will not be able to supply adequate power to connected storage devices. An iPhone with a USB-C port is an entirely different proposition - as with a suitable USB-C hub, you can connect multiple USB devices to your iPhone.
The external storage device will obviously require an appropriate USB cable to connect to the USB port of the Lightning to USB3 Camera Adapter, or a power USB hub if used.
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. APFS or HFS+ are also supported by iPad and Mac. NTFS and other proprietary formats are not supported by iPadOS.
Some additional information 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