@McChen I ran this tool on an Alder Lake setup with i9-12900K and Z690 Formula, as well as on an AMD R9 7950X and ROG 670E Hero-based system with basic/clean installs and the drive in PCIe slot 1 on each. Something on your systems may be stopping the process from locking the needed file/files due to background apps/services. On my systems, the pcie_dll.dll does not get created in the folder where the tool runs, either. Regardless, we should be getting a new tool for you to try around the end of next week. Drives with BiCS flash do not need updating. It is only for certain batches of B47R models.
As for the USB4 adapter, that should work - as you mentioned, the PCIe tunneling aspect is usually supported. If the enclosure was not USB4, say a USB 3.2 adapter instead, no drive update would work at all. I have also performed a few drive updates on Intel-based TB adapters in the past, but just not this specific one, nor with an ASMedia-based enclosure. Hopefully, the next tool will sort things out for you.
Now addressing the disconnects underload comment - typically, that points to the enclosure/host port at fault, not the drive, especially when temperatures are within operating range. After working with multiple ASM2464PD enclosures, I have also noticed the same issue with stability under little to high loads, especially with the higher capacity drives. Sometimes the host port firmware needs updating, others are the enclosure's firmware, but sometimes the enclosure's PCB design is at fault or even the cable, too. Potentially, the bridge chip or PMIC on the enclosure is overheating when the drive goes offline, but I can't say for sure. Normally, firmware addresses it. Power management can be tricky. The drive just says it needs power, and if the enclosure can't provide, it will go offline, or the link will be reset.