Explore adding explicit check for web tests that projects are public

We should consider adding a safeguard for all web tests that require public available projects. It will help to quickly debug issues and guide users to follow troubleshooting steps https://gitlab.com/gitlab-org/quality/performance/-/blob/master/docs/k6.md#tests-failing-due-to-sign-in-page-redirect.

The complication is that we will need to do this check for all projects. It should be fine for large projects but for horizontal data with thousands of projects it could become more difficult. As a first iteration, we can add the check only for large projects.