It can be countable for the 'b' definition. A work of art, for example. Or the works of Shakespeare. I think it would be unusual to make it countable in the 'a' sense, but there may be some examples.

Hi Dinghui, Teacher Tim gave you a good answer. Note that a) is something we cannot necessarily limit. For example, "he is doing work to the best of his ability". We can't count his ability or limit it, in a relative sense. Note that b) is something that is limited in what we are describing therefore it is countable. For example, "a work of art."

I think both definitions can be both count and uncountable. For meaning (a), it’s often combined with an adjective. My grandfather worked on several public works projects. He’s president of a foundation that funds charitable works. The speaker has a choice to view the work as one thing, or a collection of many things, and can choose accordingly. E.g. They fund charitable work.