Wouldn’t communism not have a worker’s state anymore? Isn’t productivity kind of just a toxic hold over to be excised once the dictatorship of the proletariat is no longer necessary?

People still need to eat, drink and fulfill their other basic needs. "Productive" here does not mean to produce much of something with the least amount of resources possible, but to contribute to the fulfillment of society's needs.

Also, what counts as production? Isn’t something produced just anything with a use-value? Isn’t sex technically a thing with a use-value?

No. The commodification of human relationships is one of the worst blights that exists in this world, and whoever aims to prolongue it is an enemy of socialism. As long as one sees human interactions as something to bbe bought and sold, they will be unable to understand what the liberation of the working people entails.

(also, where’s the line between social parasitism and just being disabled? If someone can’t work, wouldn’t that mean that by this framework they deserve to either live without anything except bare necessities, or die from starvation?)

From each according to their ability, to each according to their needs. You are comparing (in a frankly offensive manner) those who cannot work to those who are not willing to work.