Avoiding ESD on a new Graphics Card?
Bad plan because:

no one does it that way because it is not needed

you could cause other problems by making extra connections

The best way to do this is like in your picture but without connecting anything to the graphics card. Personally I would also not connect anything to the PC case because if you place it on the ESD mat, it is sufficiently grounded already.

You're worrying too much about ESD like many people do who do not understand ESD.

A graphics card by itself is not even that sensitive to ESD, you'd have to do crazy things to damage it by ESD. The same is true for the PC's motherboard. With your wristwrap + ESD mat and proper grounding I don't believe you are even capable to destroy anything as no charge buildup can occur.

When you pick up the graphics card and it is charged, it will discharge via you and your ESD wriststrap. You can also place it on the ESD mat and any charge can flow away.