Feature Request - Support mutual TLS when calling the GitLab API

When GitLab has been configured to require mTLS and Pages is on a separate host and using customer domains, calls to the GitLab internal API from Pages will be rejected.

For customers who require mTLS, it would be useful to add support mTLS for this call.

Similar work was done for Gitaly calls under gitlab#37090 (closed)

Implementation plan

• Add support in GitLab Pages: !978 (merged)
• Update Pages version: gitlab!152890 (merged)
• Add parameter in Omnibus: omnibus-gitlab!7583 (merged)
• Update docs: gitlab!152909 (merged)

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Charts implementation is tracked in this issue: gitlab#463033 (closed)

It has been concluded that charts do not support mTLS.