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.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;