test(proxy): add PATCH forwarding and absent Content-Length coverage

Closes the two untested code paths flagged in review:
- PATCH method routes to backend with correct URL
- Requests without Content-Length header pass through (NaN > n = false)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/routes/api/[...path]/proxy.spec.ts

@@ -2,7 +2,7 @@ import { describe, it, expect, vi } from 'vitest';
 
 process.env.API_INTERNAL_URL = 'http://backend:8080';
 
-const { GET, PUT, POST } = await import('./+server');
+const { GET, PUT, POST, PATCH } = await import('./+server');
 
 function makeEvent(
 	path: string,
@@ -69,6 +69,21 @@ describe('catch-all API proxy — body size limit', () => {
 		expect(mockFetch).not.toHaveBeenCalled();
 	});
 
+	it('forwards request when Content-Length header is absent', async () => {
+		const mockFetch = vi.fn().mockResolvedValue(new Response('{}', { status: 200 }));
+		const event = makeEvent('documents', 'POST', mockFetch);
+		(event.request as Request) = new Request('http://localhost/api/documents', {
+			method: 'POST',
+			headers: { 'Content-Type': 'application/json' },
+			body: JSON.stringify({ title: 'hello' })
+		});
+
+		const response = await POST(event as never);
+
+		expect(response.status).toBe(200);
+		expect(mockFetch).toHaveBeenCalled();
+	});
+
 	it('does not reject request with Content-Length exactly at 1 MB', async () => {
 		const mockFetch = vi.fn().mockResolvedValue(new Response('{}', { status: 200 }));
 		const event = makeEvent('documents', 'POST', mockFetch);
@@ -153,4 +168,22 @@ describe('catch-all API proxy — forwarding', () => {
 
 		expect(response.headers.get('Transfer-Encoding')).toBeNull();
 	});
+
+	it('forwards PATCH request to backend with correct URL', async () => {
+		const mockFetch = vi.fn().mockResolvedValue(new Response('{}', { status: 200 }));
+		const event = makeEvent('documents/doc-1', 'PATCH', mockFetch);
+		(event.request as Request) = new Request('http://localhost/api/documents/doc-1', {
+			method: 'PATCH',
+			headers: { 'Content-Type': 'application/json' },
+			body: JSON.stringify({ title: 'updated' })
+		});
+
+		const response = await PATCH(event as never);
+
+		expect(mockFetch).toHaveBeenCalledWith(
+			'http://backend:8080/api/documents/doc-1',
+			expect.objectContaining({ method: 'PATCH' })
+		);
+		expect(response.status).toBe(200);
+	});
 });