I think it's usable for both the signing of a contract as well as the combined act of drafting and signing. Usually the sense of "creating" a legal document without signing it is referred to as "drafting" or "drawing up" the contract; I don't think I've ever heard "inking" used in that sense.

You write it in ink, yes; but you also sign it in ink. That's the more definitive and final action, and represents when a thing actually occurs.

For instance, a football player can "ink" a contract to play for a team; this is almost certainly meant in the "signed" sense, as the team almost certainly wrote it. And two companies can "ink" a contract to work together or merge or whatever, and almost certainly that contract was both written and signed by those companies' representatives. But a lawyer who wrote a contract (like a will) which someone else signed wouldn't have "inked" it, but rather "drawn it up."

Doesn't inking something mean you write it in ink

It can, but it can also be used as a colloquialism for ANY way of entering a contract, even digitally (with your fingers 😉)