chore: update package dependencies and Playwright config

Update root, API, and web package.json files with latest dependencies.
Refresh pnpm-lock.yaml and update Playwright configuration.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

playwright.config.ts

@@ -41,7 +41,7 @@ export default defineConfig({
       name: 'api',
       testDir: './e2e/api',
       use: {
-        baseURL: process.env.API_BASE_URL ?? 'http://localhost:3001/api/v1',
+        baseURL: process.env.API_BASE_URL ?? 'http://localhost:3001/api/v1/',
       },
     },
     // Web E2E tests — Chromium browser