SOLR-17885: Fix authentication for new UI in browser

[malliaridis]

https://issues.apache.org/jira/browse/SOLR-17885

Description

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Solution

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This PR depends on #3703.

Tests

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Checklist

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• I have reviewed the guidelines for How to Contribute and my code conforms to the standards described there to the best of my ability.
• I have created a Jira issue and added the issue ID to my pull request title.
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• I have developed this patch against the main branch.
• I have run ./gradlew check.
• I have added tests for my changes.
• I have added documentation for the Reference Guide

[epugh]

LGTM. thanks for the tests!