test(e2e): add Playwright system smoke and regression suite

Covers: health, auth guards, register/login/token flow, every
protected page render with per-page uncaught-error capture, devices
modal wiring, stats tabs, docs pages, theme switch persistence,
reader links against real library content, security header presence,
and explicit regression assertions for the functions removed in the
dead-code cycle (Clear Queue button, queue endpoints).

package.json

@@ -25,6 +25,7 @@
     "turndown-plugin-gfm": "^1.0.2"
   },
   "devDependencies": {
+    "@playwright/test": "^1.64.1",
     "@tailwindcss/forms": "^0.5.11",
     "@tailwindcss/typography": "^0.5.19",
     "@types/turndown": "^5.0.6",