fix(gui): inject bearer token into streaming chat/research routes (#499)

Ensures that the desktop GUI correctly sends the Authorization header
when an API key is configured. This resolves the 'Failed to get response'
bug on Windows systems with enabled authentication.

Ref: #266

Co-authored-by: sanjayravit <sanjay@example.com>

frontend/src/lib/sse.ts

@@ -1,5 +1,5 @@
 import type { ResearchEvent, SSEEvent } from '../types';
-import { getBase } from './api';
+import { getBase, authHeaders } from './api';
 
 export interface ChatRequest {
   model: string;
@@ -16,7 +16,7 @@ export async function* streamChat(
   const base = getBase();
   const response = await fetch(`${base}/v1/chat/completions`, {
     method: 'POST',
-    headers: { 'Content-Type': 'application/json' },
+    headers: authHeaders({ 'Content-Type': 'application/json' }),
     body: JSON.stringify(request),
     signal,
   });
@@ -67,7 +67,7 @@ export async function* streamResearch(
   const base = getBase().replace(/\/v1\/?$/, '');
   const response = await fetch(`${base}/api/research`, {
     method: 'POST',
-    headers: { 'Content-Type': 'application/json' },
+    headers: authHeaders({ 'Content-Type': 'application/json' }),
     body: JSON.stringify({ query }),
     signal,
   });
@@ -106,3 +106,4 @@ export async function* streamResearch(
     reader.releaseLock();
   }
 }
+