A night in on purpose counts as plans. You don’t have to invent a cousin’s birthday.

Choosing to stay home is a plan, but it rarely gets reported as one, so people invent a reason with a family member in it. The invention is the tell: somewhere along the way resting became the thing that needs an excuse, while being out needs none. Your own evening is a legitimate answer. The excuse is also the part that gets you caught.

Next time, try the plain version: I am staying in tonight. No cousin, no invented shift, no sorry. Most people accept it immediately, which is slightly annoying after all the explanations you had prepared.