I fought with this for weeks on my iPhone 16 Pro. I even went and bought a fancy new USB-C cable from the Apple store (which didn't help) because none of my existing USB-C and thunderbolt cables were allowing my Sandisk Extreme Pro 4TB to work. Sometimes the drive would be available, but at USB2 speeds. Most times it just wouldn't show up at all.
Someone else early in this thread had the answer, though. The iPhone USB-C port doesn't provide enough wattage to reliably power many external storage devices. Connecting the storage through a powered USB3 hub fixed all my problems. Now the external storage shows up all the time, and runs lightning fast. Any of my thunderbolt or USB 3.2 wires work just fine. I can record ProRes 4k120 for over an hour with zero problems.