I tried a different Windows 10 laptop that did not have the Arduino IDE installed. Plugging in the board, the Device Manager listed the micronucleus USB device.
I then installed the Arduino IDE and then the ATTinyCore library from drazzy.com, which successfully installed the Windows drivers.
I unplugged the ATTiny85 MCU and attempted to compile/upload a small sketch. The IDE returned the same error 135 on the first run.
I then plugged the board in, figuring "what the heck", and attempted the upload again. This time the IDE prompted for the board to be plugged in. I unplugged it and plugged it in again and, voila, the upload was successful.
Turning back to my desktop Windows 10 PC, I uninstalled Arduino and the various Windows drivers. I reinstalled Arduino. The ATTinyCore appeared to still be installed. I removed it via the board manager and reinstalled it, which installed the drivers. Attempting to upload a sketch still gets the same upload error 135, despite following the same steps as with the laptop.
Suspecting that perhaps something lingered in the weeds, I uninstalled Arduino and the associated Windows drivers again. I also renamed my documents\arduino directory so it wouldn't be used again (presumably).
I reinstalled Arduino but found that the preferences were again unchanged from before (i.e. drazzy still included in the the board managers URL). I removed and reinstalled the ATTinyCore board/drivers as before. As before, the drivers were successfully installed.

I selected the ATTiny85 (micronecleus) board again and attempted to upload again, following the same steps as with the laptop. Still, I get error 135 regardless of whether the board is plugged in or not and regardless of which USB port it's plugged into.
The verbose upload information logged is as follows.
"C:\Users\karlh\AppData\Local\Arduino15\packages\ATTinyCore\tools\micronucleus\2.5-azd1b/micronucleus" --no-ansi --run --timeout 60 C:\Users\karlh\AppData\Local\Temp\arduino\sketches\896E47366FEDC5124B40C2B72B2FB83E/sketch_sep1a.ino.hex
Failed uploading: uploading error: exit status 0xc0000135