feat: migrate app to local Fastify and Postgres stack

Replace Supabase auth and search runtime with a local Fastify API, PostgreSQL/PostGIS schema, and local session handling. Scaffold the worker and deep-research foundations while keeping the existing research, dashboard, and map flows running on the new backend.

src/lib/api.ts

@@ -0,0 +1,28 @@
+const apiBaseUrl = import.meta.env.VITE_API_BASE_URL ?? '';
+
+export const hasApiConfig = Boolean(apiBaseUrl);
+
+export async function apiRequest<T>(path: string, init?: RequestInit): Promise<T> {
+  if (!apiBaseUrl) {
+    throw new Error('VITE_API_BASE_URL is not configured.');
+  }
+
+  const response = await fetch(`${apiBaseUrl}${path}`, {
+    credentials: 'include',
+    headers: {
+      'Content-Type': 'application/json',
+      ...(init?.headers ?? {}),
+    },
+    ...init,
+  });
+
+  const contentType = response.headers.get('content-type') || '';
+  const payload = contentType.includes('application/json') ? ((await response.json()) as unknown) : null;
+
+  if (!response.ok) {
+    const message = payload && typeof payload === 'object' && 'error' in payload ? String(payload.error) : 'Request failed.';
+    throw new Error(message);
+  }
+
+  return payload as T;
+}