Clarify auth header destiny during the redirect

[greshilov]

What do these changes do?

Backport of the #5848, but without the breaking change, just doc and test.

Are there changes in behavior for the user?

No.

Related issue number

Resolves #5783

Checklist

• I think the code is well written
• Unit tests for the changes exist
• Documentation reflects the changes
• If you provide code modification, please add yourself to CONTRIBUTORS.txt
  • The format is <Name> <Surname>.
  • Please keep alphabetical order, the file is sorted by names.
• Add a new news fragment into the CHANGES folder
  • name it <issue_id>.<type> for example (588.bugfix)
  • if you don't have an issue_id change it to the pr id after creating the pr
  • ensure type is one of the following:
    • .feature: Signifying a new feature.
    • .bugfix: Signifying a bug fix.
    • .doc: Signifying a documentation improvement.
    • .removal: Signifying a deprecation or removal of public API.
    • .misc: A ticket has been closed, but it is not of interest to users.
  • Make sure to use full sentences with correct case and punctuation, for example: "Fix issue with non-ascii contents in doctest text files."

[greshilov]

@webknjaz PTAL