chore: remove direct dependency on playwright-core

@playwright/test was already pulling playwright-core in, and its version is 1.58.1. On top of that, we pulled in 1.58.0 - unnecessarily adding ~9 MB download

Author: wojtekmaj

package.json

@@ -117,7 +117,6 @@
     "lint-staged": "16.2.7",
     "oxfmt": "0.27.0",
     "oxlint": "1.42.0",
-    "playwright-core": "1.58.0",
     "schema-dts": "1.1.5",
     "simple-git-hooks": "2.13.1",
     "typescript": "5.9.3",