feat: Add merge conflict detection and agent resolution in initiative review

Pre-merge mergeability check via `git merge-tree --write-tree` (dry-run, no
side effects). When conflicts exist the "Merge & Push" button is disabled and
a ConflictResolutionPanel shows conflict files with options to resolve manually
or spawn a conflict-resolution agent. Agent questions appear inline via
QuestionForm; on completion the mergeability re-checks automatically.

New server-side: MergeabilityResult type, BranchManager.checkMergeability,
conflict-resolution prompt, checkInitiativeMergeability query,
spawnConflictResolutionAgent mutation, getActiveConflictAgent query.

New frontend: useConflictAgent hook, ConflictResolutionPanel component,
mergeability badge + panel integration in InitiativeReview.

apps/server/git/branch-manager.ts

@@ -6,7 +6,7 @@
  * a worktree to be checked out.
  */
 
-import type { MergeResult, BranchCommit } from './types.js';
+import type { MergeResult, MergeabilityResult, BranchCommit } from './types.js';
 
 export interface BranchManager {
   /**
@@ -68,4 +68,11 @@ export interface BranchManager {
    * Defaults to 'origin' if no remote specified.
    */
   pushBranch(repoPath: string, branch: string, remote?: string): Promise<void>;
+
+  /**
+   * Dry-run merge check — determines if sourceBranch can be cleanly merged
+   * into targetBranch without actually performing the merge.
+   * Uses `git merge-tree --write-tree` (git 2.38+).
+   */
+  checkMergeability(repoPath: string, sourceBranch: string, targetBranch: string): Promise<MergeabilityResult>;
 }

apps/server/git/index.ts

@@ -13,7 +13,7 @@
 export type { WorktreeManager } from './types.js';
 
 // Domain types
-export type { Worktree, WorktreeDiff, MergeResult } from './types.js';
+export type { Worktree, WorktreeDiff, MergeResult, MergeabilityResult } from './types.js';
 
 // Adapters
 export { SimpleGitWorktreeManager } from './manager.js';

apps/server/git/simple-git-branch-manager.ts

@@ -11,7 +11,7 @@ import { mkdtempSync, rmSync } from 'node:fs';
 import { tmpdir } from 'node:os';
 import { simpleGit } from 'simple-git';
 import type { BranchManager } from './branch-manager.js';
-import type { MergeResult, BranchCommit } from './types.js';
+import type { MergeResult, MergeabilityResult, BranchCommit } from './types.js';
 import { createModuleLogger } from '../logger/index.js';
 
 const log = createModuleLogger('branch-manager');
@@ -164,4 +164,41 @@ export class SimpleGitBranchManager implements BranchManager {
     await git.push(remote, branch);
     log.info({ repoPath, branch, remote }, 'branch pushed to remote');
   }
+
+  async checkMergeability(repoPath: string, sourceBranch: string, targetBranch: string): Promise<MergeabilityResult> {
+    const git = simpleGit(repoPath);
+
+    try {
+      // git merge-tree --write-tree merges source INTO target virtually.
+      // Exit 0 = clean merge, non-zero = conflicts.
+      await git.raw(['merge-tree', '--write-tree', targetBranch, sourceBranch]);
+      log.debug({ repoPath, sourceBranch, targetBranch }, 'merge-tree check: clean');
+      return { mergeable: true };
+    } catch (err) {
+      const stderr = err instanceof Error ? err.message : String(err);
+
+      // Parse conflict file names from "CONFLICT (content): Merge conflict in <path>"
+      const conflictPattern = /CONFLICT \([^)]+\): (?:Merge conflict in|.* -> )(.+)/g;
+      const conflicts: string[] = [];
+      let match: RegExpExecArray | null;
+      while ((match = conflictPattern.exec(stderr)) !== null) {
+        conflicts.push(match[1].trim());
+      }
+
+      if (conflicts.length > 0) {
+        log.debug({ repoPath, sourceBranch, targetBranch, conflicts }, 'merge-tree check: conflicts');
+        return { mergeable: false, conflicts };
+      }
+
+      // If we couldn't parse conflicts but the command failed, it's still a conflict
+      // (could be add/add, rename conflicts, etc.)
+      if (stderr.includes('CONFLICT')) {
+        log.debug({ repoPath, sourceBranch, targetBranch }, 'merge-tree check: unparsed conflicts');
+        return { mergeable: false, conflicts: ['(unable to parse conflict details)'] };
+      }
+
+      // Genuine error (not a conflict)
+      throw err;
+    }
+  }
 }

apps/server/git/types.ts

@@ -58,6 +58,19 @@ export interface MergeResult {
   message: string;
 }
 
+// =============================================================================
+// Mergeability Check
+// =============================================================================
+
+/**
+ * Result of a dry-run merge check.
+ * No side effects — only tells you whether the merge would succeed.
+ */
+export interface MergeabilityResult {
+  mergeable: boolean;
+  conflicts?: string[];
+}
+
 // =============================================================================
 // Branch Commit Info
 // =============================================================================