[FEATURE] Cookie splitting is also needed in the proxy auth backend

[sdbruder]

Is your feature request related to a problem?
In the same way multiple auth backends implemented cookie splitting to solve big cookies issues, we are facing the same chalenge with the proxy auth backend paired with oauth2-proxy (because of the group overage thing of Entra ID). As an anedoctal point, one particular user got a 16KB cookie.

What solution would you like?
To implement the same cookie splitting already written in SAML, OpenID and JWT backends in the proxy auth backend.

What alternatives have you considered?
We tried to use OpenID directly as it supports the cookie split but it does not support group overage from Entra ID.

Do you have any additional context?
Please contact me for any further information needed.

[cwperks]

[Triage] Linking to our conversation in slack here: https://opensearch.slack.com/archives/C051Y637FKK/p1751297416762669

For anyone volunteering for this issue, this PR may be a useful reference where cookie splitting logic was applied to JWT auth type: #1651