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>

setup-windows.bat

@@ -236,9 +236,6 @@ pushd "%TARGET%"
 REM ------------------------------------------------------------------- install
 echo.
 echo  [2/6] Installing npm dependencies ^(this takes a few minutes^)...
-REM playwright is declared but unreferenced anywhere in the source; skipping its
-REM browser download saves several hundred MB and a lot of time.
-set "PLAYWRIGHT_SKIP_BROWSER_DOWNLOAD=1"
 call npm install
 if errorlevel 1 (
     echo.