fix(turn): BUG-2 addParticipant rejects duplicate id

Root cause: addParticipant appended participant to participants[] without
checking id uniqueness. Two participants with same id in array. On
togglePause resume, turnOrderIds rebuilt via sort → dup id appears twice.
nextTurn then stuck repeating that id (rotation breaks).

This was the enabling step for BUG-1's full corruption (audit chain):
  pause blocks advance → totalTurns frozen → addParticipant re-adds
  same r${totalTurns} id → resume dup → nextTurn stuck.

Fix: throw on duplicate id in addParticipant. Caller must use fresh id
(crypto.randomUUID in App, replay already does).

Evidence:
- Test: 'addParticipant rejects duplicate id' (was test.skip, now live).
- Pre-fix: 1 RED (Received function did not throw).
- Post-fix: 50 green (shared), 23 green (server), 62 green (FE).
- Reachability in normal app: low (App uses crypto.randomUUID) but no
  guard existed before. Defensive + unblocks BUG-1 isolation.

No other behavior changed.

shared/tests/turn.characterization.test.js

@@ -338,9 +338,7 @@ describe('addParticipant', () => {
     expect(patch.participants.map(x => x.id)).toEqual(['a', 'z']);
   });
 
-  // SKIPPED: RED test documenting BUG-2 (addParticipant allows dup id).
+  test('rejects duplicate id (skip-bug root cause)', () => {
-  // See TODO.md BUG-2. Re-enable (remove .skip) when fix lands.
-  test.skip('rejects duplicate id (skip-bug root cause)', () => {
     // Two participants with same id → togglePause resume rebuilds order with
     // dup id twice → nextTurn gets stuck repeating that id forever.
     // Audit found this in 100-round replay (addParticipant fired while paused

shared/turn.js

@@ -270,6 +270,9 @@ function togglePause(encounter) {
 
 // ADD_PARTICIPANT — appends participant. (Initiative rolled by caller via build*.)
 function addParticipant(encounter, participant) {
+  if ((encounter.participants || []).some(p => p.id === participant.id)) {
+    throw new Error(`Participant with id "${participant.id}" already exists in encounter.`);
+  }
   const updatedParticipants = [...(encounter.participants || []), participant];
   return {
     patch: { participants: updatedParticipants },