feat: Show resolving_conflict activity state on initiative cards

Add 'resolving_conflict' to InitiativeActivityState and detect active
conflict agents (name starts with conflict-) in deriveInitiativeActivity.
Conflict resolution takes priority over pending_review since the agent
is actively working.

- Add resolving_conflict to shared types and activity derivation
- Include conflict agents in listInitiatives agent filter (name + mode)
- Map resolving_conflict to urgent variant with pulse in InitiativeCard
- Add merge: prefix to INITIATIVE_LIST_RULES for merge event routing
- Add spawnConflictResolutionAgent to INVALIDATION_MAP
- Add getActiveConflictAgent to detail page agent: SSE invalidation

apps/server/trpc/routers/initiative-activity.ts

@@ -9,6 +9,7 @@ export interface ActiveArchitectAgent {
   initiativeId: string;
   mode: string;
   status: string;
+  name?: string;
 }
 
 const MODE_TO_STATE: Record<string, InitiativeActivityState> = {
@@ -30,6 +31,18 @@ export function deriveInitiativeActivity(
   if (initiative.status === 'archived') {
     return { ...base, state: 'archived' };
   }
+
+  // Check for active conflict resolution agent — takes priority over pending_review
+  // because the agent is actively working to resolve merge conflicts
+  const conflictAgent = activeArchitectAgents?.find(
+    a => a.initiativeId === initiative.id
+      && a.name?.startsWith('conflict-')
+      && (a.status === 'running' || a.status === 'waiting_for_input'),
+  );
+  if (conflictAgent) {
+    return { ...base, state: 'resolving_conflict' };
+  }
+
   if (initiative.status === 'pending_review') {
     return { ...base, state: 'pending_review' };
   }
@@ -41,6 +54,7 @@ export function deriveInitiativeActivity(
   // so architect agents (discuss/plan/detail/refine) surface activity
   const activeAgent = activeArchitectAgents?.find(
     a => a.initiativeId === initiative.id
+      && !a.name?.startsWith('conflict-')
       && (a.status === 'running' || a.status === 'waiting_for_input'),
   );
   if (activeAgent) {

apps/server/trpc/routers/initiative.ts

@@ -129,16 +129,16 @@ export function initiativeProcedures(publicProcedure: ProcedureBuilder) {
             : await repo.findAll();
         }
 
-        // Fetch active architect agents once for all initiatives
+        // Fetch active agents once for all initiatives (architect + conflict)
         const ARCHITECT_MODES = ['discuss', 'plan', 'detail', 'refine'];
         const allAgents = ctx.agentManager ? await ctx.agentManager.list() : [];
         const activeArchitectAgents = allAgents
           .filter(a =>
-            ARCHITECT_MODES.includes(a.mode ?? '')
+            (ARCHITECT_MODES.includes(a.mode ?? '') || a.name?.startsWith('conflict-'))
             && (a.status === 'running' || a.status === 'waiting_for_input')
             && !a.userDismissedAt,
           )
-          .map(a => ({ initiativeId: a.initiativeId ?? '', mode: a.mode ?? '', status: a.status }));
+          .map(a => ({ initiativeId: a.initiativeId ?? '', mode: a.mode ?? '', status: a.status, name: a.name }));
 
         // Batch-fetch projects for all initiatives
         const projectRepo = ctx.projectRepository;