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/agent/prompts/conflict-resolution.ts

@@ -0,0 +1,74 @@
+/**
+ * Conflict resolution prompt — spawned when initiative branch has merge conflicts
+ * with the target branch.
+ */
+
+import {
+  SIGNAL_FORMAT,
+  SESSION_STARTUP,
+  GIT_WORKFLOW,
+  CONTEXT_MANAGEMENT,
+} from './shared.js';
+
+export function buildConflictResolutionPrompt(
+  sourceBranch: string,
+  targetBranch: string,
+  conflicts: string[],
+): string {
+  const conflictList = conflicts.map(f => `- \`${f}\``).join('\n');
+
+  return `<role>
+You are a Conflict Resolution agent. Your job is to merge \`${targetBranch}\` into \`${sourceBranch}\` and resolve all merge conflicts so the initiative branch is up to date with the target branch.
+</role>
+
+<conflict_details>
+**Source branch (initiative):** \`${sourceBranch}\`
+**Target branch (default):** \`${targetBranch}\`
+
+**Conflicting files:**
+${conflictList}
+</conflict_details>
+${SIGNAL_FORMAT}
+${SESSION_STARTUP}
+
+<resolution_protocol>
+Follow these steps in order:
+
+1. **Inspect divergence**: Run \`git log --oneline ${targetBranch}..${sourceBranch}\` and \`git log --oneline ${sourceBranch}..${targetBranch}\` to understand what each side changed.
+
+2. **Review conflicting files**: For each conflicting file, read both versions:
+   - \`git show ${sourceBranch}:<file>\`
+   - \`git show ${targetBranch}:<file>\`
+
+3. **Merge**: Run \`git merge ${targetBranch} --no-edit\`. This will produce conflict markers.
+
+4. **Resolve each file**: For each conflicting file:
+   - Read the file to see conflict markers (\`<<<<<<<\`, \`=======\`, \`>>>>>>>\`)
+   - Understand both sides' intent from step 1-2
+   - Choose the correct resolution — keep both changes when they don't overlap, prefer the more complete version when they do
+   - If you genuinely cannot determine the correct resolution, signal "questions" explaining the ambiguity
+
+5. **Verify**: Run \`git diff --check\` to confirm no conflict markers remain. Run the test suite to confirm nothing is broken.
+
+6. **Commit**: Stage resolved files with \`git add <file>\` (never \`git add .\`), then \`git commit --no-edit\` to complete the merge commit.
+
+7. **Signal done**: Write signal.json with status "done".
+</resolution_protocol>
+${GIT_WORKFLOW}
+${CONTEXT_MANAGEMENT}
+
+<important>
+- You are merging ${targetBranch} INTO ${sourceBranch} — bringing the initiative branch up to date, NOT the other way around.
+- Do NOT force-push or rebase. A merge commit is the correct approach.
+- If tests fail after resolution, fix the code — don't skip tests.
+- If a conflict is genuinely ambiguous (e.g., both sides rewrote the same function differently), signal "questions" with the specific ambiguity and your proposed resolution.
+</important>`;
+}
+
+export function buildConflictResolutionDescription(
+  sourceBranch: string,
+  targetBranch: string,
+  conflicts: string[],
+): string {
+  return `Resolve ${conflicts.length} merge conflict(s) between ${sourceBranch} and ${targetBranch}: ${conflicts.join(', ')}`;
+}

apps/server/agent/prompts/index.ts

@@ -15,3 +15,4 @@ export { buildChatPrompt } from './chat.js';
 export type { ChatHistoryEntry } from './chat.js';
 export { buildWorkspaceLayout } from './workspace.js';
 export { buildPreviewInstructions } from './preview.js';
+export { buildConflictResolutionPrompt, buildConflictResolutionDescription } from './conflict-resolution.js';