Thanks for the pics
Looks like it needs 5v, 2.0 amps.
I looked at my own Samsung SE-506 BD/DVD/CD burner, and the manual states that it needs USB port current 1.4a or higher.
I'm wondering if the "2.0" amp requirement is just too much for a single USB port on the 2016 MBP?
Also... I'm wondering how the USBa/USBc adapter handles or "passes through" bus power? Perhaps that could be "getting into the mix". Could it prevent USB power from getting to the drive?
Does your drive have a "hard wired" USB cable (can't be unplugged from the back)? Or is it removable?
If it's removable, I'd try replacing it with a USBa (drive end) to USBc (Mac end) cable. That would eliminate the adapter.
Does the back of CD drive have a small input for an external power supply?
I realize it's "one more thing to carry around", but it may provide enough power to run the drive so that the Mac's USB port isn't overloaded.
Another thought:
Get a POWERED USB hub (one that comes with its own power supply), and connect that to the Mac, and then connect the drive to it.
When all is said and done, it MIGHT be "easiest and cheapest" just to buy another DVD/CD USB drive.
BUT... CHECK CAREFULLY before you buy, to be sure that the power requirements are "less than" this one...