Does the USB-C port on the Osmo Pocket 4 Threaded Handle and the Osmo Pocket 4 Battery Handle support data transfer? What cable standard is compatible, and what is the maximum transfer rate?

Yes, both ports support data transfer. When using the provided USB-C to USB-C PD Cable (USB 3.1) or another USB 3.1-compliant cable, you can export data from built-in storage at a maximum transfer rate of 800 MB/s.