Fix API-key login and research navigation

Validate submitted keys against the protected research endpoint instead of the nonexistent versioned health path. Replace server-only redirects in client code with SvelteKit navigation and route successful logins to the existing new-research screen.

Align frontend research history and creation calls with the backend response contract: list items are wrapped in items and new runs return research_id.

src/lib/sidebar.ts

@@ -16,7 +16,8 @@ export interface ResearchListItem extends ResearchSummary {
 const HISTORY_LIMIT = 50;
 
 export async function loadResearchHistory(apiKey: string): Promise<ResearchSummary[]> {
-    const list = await apiGet<ResearchSummary[]>('/v1/research', { apiKey });
+    const response = await apiGet<{ items: ResearchSummary[] }>('/v1/research', { apiKey });
+    const list = response.items;
     // Sort descending by created_at (newest first), limit to HISTORY_LIMIT
     const sorted = list
         .slice()
@@ -34,10 +35,10 @@ export async function createResearch(
     query: string,
     language: string,
     depth: string
-): Promise<{ id: string }> {
-    return await apiPost<{ id: string }>(
+): Promise<{ research_id: string }> {
+    return await apiPost<{ research_id: string }>(
         '/v1/research',
         { query, language, depth },
         { apiKey }
     );
-}
+}