Have you tried an enclosure for the drive with its own dedicated power source?
My suspicion is that upon the PD renegotiation, your drive is temporarily losing power. Whether this is expected or USB-compliant behavior, I don’t know. But if that is the problem, I’d think using a separately powered enclosure might solve it.
On the other hand, maybe the (internal to hub) data hub IC is resetting the data line upon PD renegotiation. That seems contrary to the intent of USB and I’d suspect violates the USB standard.
Source: I’ve designed some USB PD power systems but not delved into the details of how data is handled