feat: implement POST /pulls merge handler with merge button in PR detail

Add MergePull HTTP handler that calls the existing client.MergePull()
method, register the POST /pulls/{owner}/{repo}/{index}/merge route,
and add a merge button/form to the PR detail template gated on
Mergeable and open state. Supports merge, rebase, and squash styles.

- Handler returns HTMX fragment on HX-Request, redirect otherwise
- Error path returns inline error fragment for HTMX requests
- Add mock merge endpoint and 3 integration tests
- Merge button only shows when PR is mergeable and open

Closes leeworks-agents/gitea-mobile#229

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

internal/handlers/integration_test.go

@@ -185,6 +185,11 @@ func mockGiteaAPI(t *testing.T) *httptest.Server {
 		json.NewEncoder(w).Encode(map[string]interface{}{"id": 1, "state": "APPROVED"})
 	})
 
+	// POST /api/v1/repos/{owner}/{repo}/pulls/{index}/merge — merge PR.
+	mux.HandleFunc("POST /api/v1/repos/{owner}/{repo}/pulls/{index}/merge", func(w http.ResponseWriter, r *http.Request) {
+		w.WriteHeader(http.StatusOK)
+	})
+
 	// POST /api/v1/markdown — render markdown.
 	mux.HandleFunc("POST /api/v1/markdown", func(w http.ResponseWriter, r *http.Request) {
 		w.Header().Set("Content-Type", "text/html")
@@ -917,6 +922,67 @@ func TestIntegration_SubmitReview_RequestChanges(t *testing.T) {
 	}
 }
 
+// --- Issue #229: Integration tests for POST /pulls/{owner}/{repo}/{index}/merge ---
+
+func TestIntegration_MergePull_Valid(t *testing.T) {
+	h, srv := newTestHandlerWithMock(t)
+	defer srv.Close()
+
+	mux := http.NewServeMux()
+	mux.HandleFunc("POST /pulls/{owner}/{repo}/{index}/merge", h.MergePull)
+
+	form := url.Values{"Do": {"merge"}}
+	req := reqWithToken(http.MethodPost, "/pulls/test-org/repo1/1/merge", form.Encode())
+	w := httptest.NewRecorder()
+
+	mux.ServeHTTP(w, req)
+
+	if w.Code != http.StatusSeeOther {
+		t.Errorf("status = %d, want %d", w.Code, http.StatusSeeOther)
+	}
+}
+
+func TestIntegration_MergePull_HTMX(t *testing.T) {
+	h, srv := newTestHandlerWithMock(t)
+	defer srv.Close()
+
+	mux := http.NewServeMux()
+	mux.HandleFunc("POST /pulls/{owner}/{repo}/{index}/merge", h.MergePull)
+
+	form := url.Values{"Do": {"squash"}}
+	req := reqWithToken(http.MethodPost, "/pulls/test-org/repo1/1/merge", form.Encode())
+	req.Header.Set("HX-Request", "true")
+	w := httptest.NewRecorder()
+
+	mux.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("status = %d, want %d", w.Code, http.StatusOK)
+	}
+	body := w.Body.String()
+	if !contains(body, "Merged") {
+		t.Errorf("expected 'Merged' in HTMX response, got: %s", body)
+	}
+}
+
+func TestIntegration_MergePull_DefaultStyle(t *testing.T) {
+	h, srv := newTestHandlerWithMock(t)
+	defer srv.Close()
+
+	mux := http.NewServeMux()
+	mux.HandleFunc("POST /pulls/{owner}/{repo}/{index}/merge", h.MergePull)
+
+	// No "Do" form value — should default to "merge".
+	req := reqWithToken(http.MethodPost, "/pulls/test-org/repo1/1/merge", "")
+	w := httptest.NewRecorder()
+
+	mux.ServeHTTP(w, req)
+
+	if w.Code != http.StatusSeeOther {
+		t.Errorf("status = %d, want %d", w.Code, http.StatusSeeOther)
+	}
+}
+
 // --- Issue #110: Integration tests for POST /issues/{owner}/{repo}/{index}/labels ---
 
 func TestIntegration_ApplyLabels_Valid(t *testing.T) {