type safety: complete catch(err:unknown) migration + extract admin routes

- All remaining catch(err) and catch(error) blocks now use : unknown
  across keys.ts, email.ts, usage.ts, index.ts (shutdown handlers)
- Extract admin/usage routes from index.ts (459→391 lines) into
  new src/routes/admin.ts with authMiddleware + adminAuth per-route
- Remove unused imports from index.ts (getConcurrencyStats, isProKey,
  getUsageForKey, getUsageStats, NextFunction)
- 10 new TDD tests (7 error helper, 3 admin router)
- 608 total tests, all passing

src/__tests__/admin-routes.test.ts

@@ -0,0 +1,19 @@
+import { describe, it, expect } from "vitest";
+import { adminRouter } from "../routes/admin.js";
+
+describe("admin router extraction", () => {
+  it("exports adminRouter", () => {
+    expect(adminRouter).toBeDefined();
+  });
+
+  it("adminRouter is an Express Router", () => {
+    // Express routers have a stack property
+    expect((adminRouter as any).stack).toBeDefined();
+    expect(Array.isArray((adminRouter as any).stack)).toBe(true);
+  });
+
+  it("has routes registered", () => {
+    const stack = (adminRouter as any).stack;
+    expect(stack.length).toBeGreaterThan(0);
+  });
+});

src/__tests__/catch-type-safety.test.ts

@@ -0,0 +1,35 @@
+import { describe, it, expect } from "vitest";
+import { errorMessage, errorCode } from "../utils/errors.js";
+
+describe("catch type safety helpers", () => {
+  it("errorMessage handles Error instances", () => {
+    expect(errorMessage(new Error("test error"))).toBe("test error");
+  });
+
+  it("errorMessage handles string errors", () => {
+    expect(errorMessage("raw string error")).toBe("raw string error");
+  });
+
+  it("errorMessage handles non-Error objects", () => {
+    expect(errorMessage({ code: "ENOENT" })).toBe("[object Object]");
+  });
+
+  it("errorMessage handles null/undefined", () => {
+    expect(errorMessage(null)).toBe("null");
+    expect(errorMessage(undefined)).toBe("undefined");
+  });
+
+  it("errorCode extracts code from Error with code", () => {
+    const err = Object.assign(new Error("fail"), { code: "ECONNREFUSED" });
+    expect(errorCode(err)).toBe("ECONNREFUSED");
+  });
+
+  it("errorCode returns undefined for plain Error", () => {
+    expect(errorCode(new Error("no code"))).toBeUndefined();
+  });
+
+  it("errorCode returns undefined for non-Error", () => {
+    expect(errorCode("string error")).toBeUndefined();
+    expect(errorCode(42)).toBeUndefined();
+  });
+});