I’m designing a board in Eagle with part TLC5971 whose footprint includes a thermal pad (EPAD pin 21 - see attachment). Should this be connected to GND? Do I need to add any vias within the pad’s area?
Hard to say, it depends on the part.
The data sheet should have information on what the pad connects too. If the pad is connected to ground internally, you probably should ground the pad on your PCB too. Some are isolated and in that case, it probably doesn’t matter but grounding it wouldn’t be a bad idea.