Complete Story 1-1 and fix TypeScript issues

Add TypeScript strict mode and typecheck tasks to monorepo infrastructure.
Fix E2E test @payload-config alias and frontend TypeScript errors.

- Add tsconfig.json to backend with strict mode and path aliases
- Add typecheck task to Turborepo and all packages
- Fix @payload-config alias for E2E tests and dev server
- Add setToken method to AuthService for middleware use
- Fix implicit any types in Footer.astro and Header.astro
- Remove invalid typescript config from astro.config.mjs

apps/frontend/src/components/Header.astro

@@ -135,7 +135,7 @@ import { Image } from "astro:assets";
             mobileNav.innerHTML = "";
 
             // Populate desktop navigation
-            navItems.forEach((item) => {
+            navItems.forEach((item: NavItem) => {
                 const linkHtml = createNavLink(item);
                 const li = document.createElement("li");
                 li.innerHTML = linkHtml;
@@ -143,7 +143,7 @@ import { Image } from "astro:assets";
             });
 
             // Populate mobile navigation
-            navItems.forEach((item) => {
+            navItems.forEach((item: NavItem) => {
                 const linkHtml = createNavLink(item)
                     .replace("px-3 py-2", "block px-3 py-2")
                     .replace(