chore: remove direct dependency on playwright-core (#898)

Author: wojtekmaj

package.json

@@ -116,7 +116,6 @@
     "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",