I didn’t consider ground loops, so I will interconnect both ground bars on the entrance or I will keep one single ground bar for all circuits, new and old.Terminology: Ground ROD is in the earth and connects to the Panel Neutral BAR which connects to Transformer Neutral.
There’s more to ground rods than just sticking a piece of copper in the ground.
Adding two rods could reduce their efficacy in the event of a lightning strike, their primary purpose.
If materials differ, you could set up a galvanic cell which would eat one away. Ditto if perchance soil & moisture conditions differ dramatically at the two locations. Unlikely in a home installation but not outside the realm of possibility.
The 3rd pin is a secondary SAFETY path to return fault current to the transformer neutral to ensure enough current flows to trip the breaker. If you don’t return the 3rd pin to the transformer neutral YOUR SYSTEM IS LETHAL!