How much notice is reasonable when the handover is complex

Whatever the contract says, plus a written handover that outlives you: runbooks, access list, the three things that break at 3am. Extending the notice period rarely helps; writing things down always does.

Offer a substitute rather than a refusal: a take-home you have already done, a walkthrough of public work, or pair debugging on their codebase. Companies that decline all three have told you something useful about how they work.

Timebox the unknown separately. Estimate the known work normally, then add an explicit investigation slot with a decision point at the end. Merging the two produces a number that is wrong in a way nobody can inspect.