fix(web): skip empty Authorization header for forward-auth proxy compatibility

Centralize duplicated getToken() + Bearer header logic into a single
formatHeaders() helper in lib/api.ts. When no token exists, the
Authorization header is omitted entirely instead of sending an empty
Bearer token, which breaks forward-auth proxies like Authelia behind
Caddy.

Changes:
- Add formatHeaders() with try-catch around localStorage access
- Replace 20+ duplicated getToken() definitions across tool components
- Migrate all call sites including file-details, settings, change-password
- Update tests to verify header omission on empty token

Based on the fix proposed by @jules2689 in #6, with improvements:
file placement (lib/api.ts vs components), localStorage error handling,
simplified truthiness check, and complete call-site coverage.

Co-Authored-By: Julian Nadeau <julian@jnadeau.ca>

apps/web/src/components/tools/split-settings.tsx

@@ -1,11 +1,7 @@
 import { Download, Loader2 } from "lucide-react";
 import { useState } from "react";
+import { formatHeaders } from "@/lib/api";
 import { useFileStore } from "@/stores/file-store";
-
-function getToken(): string {
-  return localStorage.getItem("stirling-token") || "";
-}
-
 export function SplitSettings() {
   const { files, processing, error, setProcessing, setError } = useFileStore();
   const [columns, setColumns] = useState(2);
@@ -26,7 +22,7 @@ export function SplitSettings() {
 
       const res = await fetch("/api/v1/tools/split", {
         method: "POST",
-        headers: { Authorization: `Bearer ${getToken()}` },
+        headers: formatHeaders(),
         body: formData,
       });