In v16.8.0 - namespace_in_path and access_control both are enabled, Private Pages urls gives 401 after auth

Summary

In omnibus installation:

• GitLab Pages: enabled
• GitLab Pages access control: enabled
• GitLab Pages namespace_in_path: enabled
• Project Path: https://example.gitlab.com/group/testproject
• Pages Domain: https://pages.example.gitlab.com

... and it works on v16.7.3 then upgraded to v16.8.0 and GitLab Pages Access Control does not work like when namespace_in_path are enabled

More details: #434372 (comment 1738176906)

Steps to reproduce

Example Project

What is the current bug behavior?

What is the expected correct behavior?

Relevant logs and/or screenshots

Output of checks

Results of GitLab environment info

Expand for output related to GitLab environment info

(For installations with omnibus-gitlab package run and paste the output of: \`sudo gitlab-rake gitlab:env:info\`) (For installations from source run and paste the output of: \`sudo -u git -H bundle exec rake gitlab:env:info RAILS_ENV=production\`)

Results of GitLab application Check

Expand for output related to the GitLab application check

(For installations with omnibus-gitlab package run and paste the output of: `sudo gitlab-rake gitlab:check SANITIZE=true`)

(For installations from source run and paste the output of: `sudo -u git -H bundle exec rake gitlab:check RAILS_ENV=production SANITIZE=true`)

(we will only investigate if the tests are passing)

Possible fixes