feat(engagement): localize limits and streaks

Use reported user timezones for daily response limits, expose couple streak state and reminders, and improve swipe and live-drawing synchronization with focused tests and documentation.

apps/api/test/answers.routes.test.ts

@@ -15,7 +15,9 @@ function app(r:AnswersRepository){const app=new Hono<{Variables:{identity:AuthId
 
 describe('answer routes',()=>{
   it('takes ownership only from the bearer identity',async()=>{const r=repo();const a=app(r);await a.request('/v1/responses',{method:'POST',headers:{'content-type':'application/json'},body:JSON.stringify({question_id:questionId,answer:'yes',user_id:'attacker'})});expect(r.submit).not.toHaveBeenCalled();const ok=await a.request('/v1/responses',{method:'POST',headers:{'content-type':'application/json'},body:JSON.stringify({question_id:questionId,answer:'yes'})});expect(ok.status).toBe(200);expect(r.submit).toHaveBeenCalledWith(identity.id,{questionId,answer:'yes',responseData:undefined});});
-  it('maps confirmation and domain failures',async()=>{const r=repo();vi.mocked(r.update).mockResolvedValueOnce({success:false,requires_confirmation:true,message_count:2});const a=app(r);expect(await (await a.request(`/v1/responses/${questionId}`,{method:'PATCH',headers:{'content-type':'application/json'},body:'{"new_answer":"no"}'})).json()).toMatchObject({requires_confirmation:true,message_count:2});vi.mocked(r.submit).mockRejectedValueOnce(new AnswersError('daily_limit',429,'Daily response limit reached'));expect((await a.request('/v1/responses',{method:'POST',headers:{'content-type':'application/json'},body:JSON.stringify({question_id:questionId,answer:'yes'})})).status).toBe(429);});
+  it('maps confirmation and domain failures',async()=>{const r=repo();vi.mocked(r.update).mockResolvedValueOnce({success:false,requires_confirmation:true,message_count:2});const a=app(r);expect(await (await a.request(`/v1/responses/${questionId}`,{method:'PATCH',headers:{'content-type':'application/json'},body:'{"new_answer":"no"}'})).json()).toMatchObject({requires_confirmation:true,message_count:2});vi.mocked(r.submit).mockRejectedValueOnce(new AnswersError('daily_limit',429,'Daily response limit reached',{daily_limit:10,responses_today:10,remaining:0,reset_at:'2026-08-29T00:00:00.000Z'}));const blocked=await a.request('/v1/responses',{method:'POST',headers:{'content-type':'application/json'},body:JSON.stringify({question_id:questionId,answer:'yes'})});expect(blocked.status).toBe(429);
+    // The client renders the limit screen straight from this body, so its shape is a contract.
+    expect(await blocked.json()).toMatchObject({error:{code:'daily_limit'},details:{daily_limit:10,responses_today:10,remaining:0,reset_at:'2026-08-29T00:00:00.000Z'}});});
   it('scopes match mutations to identity',async()=>{const r=repo();const a=app(r);await a.request('/v1/matches/seen',{method:'PATCH',headers:{'content-type':'application/json'},body:JSON.stringify({ids:[questionId]})});expect(r.markSeen).toHaveBeenCalledWith(identity.id,[questionId]);await a.request(`/v1/matches/${questionId}/archive`,{method:'PUT',headers:{'content-type':'application/json'},body:'{"archived":true}'});expect(r.archive).toHaveBeenCalledWith(identity.id,questionId,true);});
 });