Turn on eslint playwright plugin and eslint react-query plugin

[tom2drum]

Description and Related Issue(s)

These rules/plugins were disabled during migration to Eslint v9. Now we updated our code and turned them on.

Checklist for PR author

• I have tested these changes locally.
• I added tests to cover any new functionality, following this guide
• Whenever I fix a bug, I include a regression test to ensure that the bug does not reappear silently.
• If I have added, changed, renamed, or removed an environment variable
  • I updated the list of environment variables in the documentation
  • I made the necessary changes to the validator script according to the guide
  • I added "ENVs" label to this pull request