fix: resolve all TypeScript strict-mode errors in test files

- convert-sanitized: use 'as Record' cast for optional mock call args
- error-responses: fix module path (database.js → db.js) and mock return type
- recover-initial-db-fallback: fix mock return type (undefined → true)
- render-timing: remove non-existent .prepare property check
- usage-flush: cast mock request objects to any for test setup

Zero tsc --noEmit errors. 608 tests passing.

src/__tests__/recover-initial-db-fallback.test.ts

@@ -63,7 +63,7 @@ describe("POST /v1/recover DB fallback (BUG-110)", () => {
     vi.clearAllMocks();
     mockGetAllKeys.mockReturnValue([]);
     mockCreatePending.mockResolvedValue({ code: "123456" } as any);
-    mockSendEmail.mockResolvedValue(undefined);
+    mockSendEmail.mockResolvedValue(true);
   });
 
   it("sends verification email via DB fallback when key not in cache but exists in DB", async () => {