feat(pairing): solo sealed answers that unlock on pairing

Unpaired users could only reach a waiting-room dead end and could not answer
questions until a partner joined. Responses.couple_id is now nullable so a
solo user answers immediately and banks "sealed answers" (couple_id IS NULL).
Pairing claims both members' sealed answers and computes matches for every
question both have now answered. Invite copy and the unpaired push nudge
escalate with the sealed answer count.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/api/test/operations.integration.test.ts

@@ -12,7 +12,7 @@ describe.skipIf(!databaseUrl||!local)('PostgresOperationsRepository',()=>{
   const pack='44444444-4444-4444-8444-444444444444',question='55555555-5555-4555-8555-555555555555';let pool:Pool;let repo:PostgresOperationsRepository;let repo2:PostgresOperationsRepository;
   beforeAll(async()=>{
     await admin.query(`create schema "${schema}"`);const url=new URL(databaseUrl!);url.searchParams.set('options',`-c search_path=${schema}`);pool=new Pool({connectionString:url.toString()});repo=new PostgresOperationsRepository(url.toString());repo2=new PostgresOperationsRepository(url.toString());
-    for(const name of ['0000_identity_and_feature_interests.sql','0001_couples.sql','0002_packs_catalog_progress.sql','0003_answers_matches.sql','0004_chat.sql','0005_profile_settings.sql','0006_media_storage.sql','0009_operations_workers.sql','0010_admin.sql','0014_daily_limit_local_reset.sql','0016_couple_streak_locality.sql','0017_streak_reminder_preference.sql']){
+    for(const name of ['0000_identity_and_feature_interests.sql','0001_couples.sql','0002_packs_catalog_progress.sql','0003_answers_matches.sql','0004_chat.sql','0005_profile_settings.sql','0006_media_storage.sql','0009_operations_workers.sql','0010_admin.sql','0014_daily_limit_local_reset.sql','0016_couple_streak_locality.sql','0017_streak_reminder_preference.sql','0021_solo_sealed_answers.sql']){
       const sql=await readFile(new URL(`../drizzle/${name}`,import.meta.url),'utf8');for(const statement of sql.split('--> statement-breakpoint'))if(statement.trim())await pool.query(statement);
     }
     await pool.query('insert into couples(id,invite_code) values($1,$2)',[couple,'ABCD2345']);
@@ -59,6 +59,22 @@ describe.skipIf(!databaseUrl||!local)('PostgresOperationsRepository',()=>{
     expect((await pool.query('select count(*)::int count from operations_outbox where dedupe_key=$1',[`discord:couple_paired:${inviteCouple}`])).rows[0].count).toBe(1);
   });
 
+  it('escalates the unpaired nudge copy with the sealed answer count',async()=>{
+    const solo=randomUUID(),secondQuestion=randomUUID();
+    await pool.query(`insert into profiles(id,name,email,push_token,onboarding_completed) values($1,'Solo','solo@test','token-solo',false)`,[solo]);
+    await pool.query('insert into questions(id,pack_id,text) values($1,$2,$3)',[secondQuestion,pack,'Second question']);
+    await pool.query(`insert into responses(id,user_id,question_id,couple_id,answer) values($1,$2,$3,null,'yes'),($4,$2,$5,null,'maybe')`,
+      [randomUUID(),solo,question,randomUUID(),secondQuestion]);
+
+    await repo.produce(new Date('2026-08-28T18:00:00.000Z'),100);
+    const body=(await pool.query<{body:string;data:{sealed_count:number}}>(
+      `select payload->>'body' body,payload->'data' data from operations_outbox where dedupe_key=$1`,
+      [`unpaired:2026-08-28:${solo}`],
+    )).rows[0];
+    expect(body?.body).toContain('2 sealed answers waiting');
+    expect(body?.data).toMatchObject({sealed_count:2});
+  });
+
   it('atomically releases packs, celebrates milestones, and produces a single digest',async()=>{
     await pool.query(`insert into couple_streaks(couple_id,current_streak,longest_streak,streak_celebrated_at) values($1,7,7,0) on conflict(couple_id) do update set current_streak=7,streak_celebrated_at=0`,[couple]);
     const result=await repo.produce(new Date(Date.now()+10*60*1000),100);