feat: add MergeDialog component and integrate with GitToolbar

- Create MergeDialog component for branch merging
- Add merge button to GitToolbar
- Show source branch selector and target branch display
- Handle merge success and error states
- Add modal CSS styles

Completes Task 6.2 of git-control change.

apps/web/src/components/git-toolbar.tsx

@@ -9,6 +9,7 @@ import {
   pushRepository,
   type GitStatus,
 } from "../api/git_repositories";
+import { MergeDialog } from "./merge-dialog";
 
 interface GitToolbarProps {
   projectId: string;
@@ -33,6 +34,7 @@ export const GitToolbar = ({
   const [showNewBranch, setShowNewBranch] = useState(false);
   const [newBranchName, setNewBranchName] = useState("");
   const [newBranchBase, setNewBranchBase] = useState("");
+  const [showMergeDialog, setShowMergeDialog] = useState(false);
 
   const loadStatus = useCallback(async () => {
     try {
@@ -179,6 +181,14 @@ export const GitToolbar = ({
             ⇡ Push
             {status?.ahead ? <span className="badge">{status.ahead}</span> : null}
           </button>
+          <button
+            className="toolbar-button"
+            onClick={() => setShowMergeDialog(true)}
+            disabled={loading}
+            type="button"
+          >
+            🔀 Merge
+          </button>
         </div>
       </div>
 
@@ -227,6 +237,19 @@ export const GitToolbar = ({
           {status.untracked.length > 0 && <span className="status-badge untracked">❓ {status.untracked.length} untracked</span>}
         </div>
       )}
+
+      <MergeDialog
+        projectId={projectId}
+        repoId={repoId}
+        branches={branches}
+        currentBranch={currentBranch}
+        isOpen={showMergeDialog}
+        onClose={() => setShowMergeDialog(false)}
+        onMerge={() => {
+          void loadStatus();
+          onRefresh();
+        }}
+      />
     </div>
   );
 };

apps/web/src/components/merge-dialog.tsx

@@ -0,0 +1,132 @@
+import { useState } from "react";
+
+import { mergeBranches } from "../api/git_repositories";
+
+interface MergeDialogProps {
+  projectId: string;
+  repoId: string;
+  branches: string[];
+  currentBranch: string;
+  isOpen: boolean;
+  onClose: () => void;
+  onMerge: () => void;
+}
+
+export const MergeDialog = ({
+  projectId,
+  repoId,
+  branches,
+  currentBranch,
+  isOpen,
+  onClose,
+  onMerge,
+}: MergeDialogProps) => {
+  const [sourceBranch, setSourceBranch] = useState("");
+  const [commitMessage, setCommitMessage] = useState("");
+  const [loading, setLoading] = useState(false);
+  const [error, setError] = useState<string | null>(null);
+  const [success, setSuccess] = useState(false);
+
+  if (!isOpen) return null;
+
+  const availableBranches = branches.filter((b) => b !== currentBranch);
+
+  const handleMerge = async () => {
+    if (!sourceBranch) {
+      setError("Please select a source branch");
+      return;
+    }
+    setLoading(true);
+    setError(null);
+    setSuccess(false);
+    try {
+      await mergeBranches(
+        projectId,
+        repoId,
+        sourceBranch,
+        currentBranch,
+        commitMessage || undefined
+      );
+      setSuccess(true);
+      setTimeout(() => {
+        onMerge();
+        onClose();
+      }, 1500);
+    } catch {
+      setError("Merge failed. There may be conflicts to resolve.");
+    } finally {
+      setLoading(false);
+    }
+  };
+
+  return (
+    <div className="modal-overlay" onClick={onClose}>
+      <div className="modal-content" onClick={(e) => e.stopPropagation()}>
+        <h2>Merge Branch</h2>
+        
+        <div className="merge-form">
+          <div className="form-field">
+            <label>Source Branch (merge from)</label>
+            <select
+              value={sourceBranch}
+              onChange={(e) => setSourceBranch(e.target.value)}
+              disabled={loading}
+            >
+              <option value="">Select branch...</option>
+              {availableBranches.map((branch) => (
+                <option key={branch} value={branch}>
+                  {branch}
+                </option>
+              ))}
+            </select>
+          </div>
+
+          <div className="form-field">
+            <label>Target Branch (merge into)</label>
+            <input
+              type="text"
+              value={currentBranch}
+              disabled
+              className="input-disabled"
+            />
+          </div>
+
+          <div className="form-field">
+            <label>Commit Message (optional)</label>
+            <textarea
+              value={commitMessage}
+              onChange={(e) => setCommitMessage(e.target.value)}
+              placeholder={`Merge ${sourceBranch || "branch"} into ${currentBranch}`}
+              rows={3}
+              disabled={loading}
+            />
+          </div>
+
+          {error && <div className="error-text">{error}</div>}
+          {success && (
+            <div className="success-text">Merge successful!</div>
+          )}
+
+          <div className="modal-actions">
+            <button
+              className="secondary-button"
+              onClick={onClose}
+              disabled={loading}
+              type="button"
+            >
+              Cancel
+            </button>
+            <button
+              className="primary-button"
+              onClick={handleMerge}
+              disabled={loading || !sourceBranch}
+              type="button"
+            >
+              {loading ? "Merging..." : "Merge"}
+            </button>
+          </div>
+        </div>
+      </div>
+    </div>
+  );
+};