at the recent PPTQ we faced following situation:
Andrew controls Watchful Naga. He turns it sideways, loudly saying “EXERT!”.
Nathan, after some time passed, blocks with his 3/2 creature, asks “Damage?”
Andrew confirms and upon putting the Naga to his graveyard says: “Oh, I should have drawn a card, so I draw now?” Nathan calls for a judge.
Is it a standard Missed trigger or a GRV (because Exert and the trigger are linked) wit possible backup?

The fact that the trigger is linked to exert doesn't matter- it's still a trigger. He announced the exertion of the creature, but he can still miss the trigger.

Andrew didn't draw the card “before taking any game actions … that can be taken only after the triggered ability should have resolved” - classic case of Missed Trigger.

If Andrew had interrupted Nathan's block by saying “oh, I get to draw”, he'd be fine. Once he allows or acknowledges the block, he's moved past the point where the trigger should have resolved.

d:^D