If you’re looking for a simple mechanic, how about starting an “Addicted” clock which, when filled, changes their vice to revolve around the substance they’ve been using? It may be pleasure, stupor, obligation (or if you want a totally focused thing, a new vice simply called Addiction), but the key is that it’s only indulgeable by using that substance?
The size of the clock is based on how addictive you think the drug is. Using the substance adds one tick, which is a side effect/consequence that can be resisted. Devil’s Bargains and normal roll consequences could add extra ticks at other times.
Easy, simple, stays within the scope the main rules.
If you want more nasty effects after addiction begins, start a new clock, like “the drug takes its toll.” When it fills (same rules as filling the original addiction clock), you figure out what that means. This could be different every time it fills, like “You wake to find all your coin is gone,” or “While you were on a bender, you beat up your key crew ally.”
Long-term projects could remove ticks from any of these clocks, or work to recover from/beat the addiction (change their vice to something else.)