Drop the unused playwright dependency

playwright was declared but referenced nowhere in the source — no import, no
require, no script. Its postinstall downloads several hundred MB of browsers
on every install, which setup-windows.bat had been working around with
PLAYWRIGHT_SKIP_BROWSER_DOWNLOAD. Removing the dependency removes the need for
the workaround, so that goes too.

Nothing else depends on it; the remaining lockfile mentions are Next declaring
@playwright/test as an optional peer, which installs nothing.

Instances pick this up through the normal update path: package-lock.json
changed, so update-check runs npm install and playwright disappears from
node_modules. Any browsers already downloaded on a machine live outside
node_modules and are not removed by this — see README.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

package.json

@@ -12,7 +12,6 @@
     "axios": "^1.13.6",
     "better-sqlite3": "^12.6.2",
     "next": "16.1.6",
-    "playwright": "^1.58.2",
     "react": "19.2.3",
     "react-dom": "19.2.3",
     "recharts": "^3.8.0"