Can I use an Ohm meter to test if the coils are still good if I disconnect the wires from the control board.
Yes, you can. There are just two coils inside, and for any stepper I’ve examined the datasheet for, the resistance is low…under 10 ohms, so just look for continuity. Note that your checks at the control board end also checks the extension wires, which I would consider a more likely culprit for your problem. Stepper motors are simple devices that rarely fail. In the dozens of forum posts I’ve read where the stepper was failing to spin or spinning poorly, I can only remember one topic where ultimately it was a bad stepper motor.
I am running a SKR Pro with the 2209 drivers.
V1 sets the current for the TMC2209 drivers in firmware, so this is not a current-too-high issue.
so I believe the board is still sending signal on the Y2 port.
You can verify this if you swap the stepper drivers and the stepper wires between Y1 and Y2. After the swap, Y1 should move.
Edit to add: The fact that Y2 did not start to move after it cooled down is a strong indication your problem is not a stepper driver overheating.