I think the distinction between "Dying with Covid. And "dying of Covid" is not particularly relevant.

"Dying with Covid" can mean someone who is dying anyway who catches Covid on their deathbed. But in most cases it means someone who had some existing condition which did not in itself threaten life, who catches Covid, and who dies.

That's a death that wouldn't have taken place without Covid just as much as that of someone who was in perfect health until they caught Covid.