Backport "Fix Classic Duo Chat UI is stuck" into 18.6-stable-ee

What does this MR do and why?

Describe in detail what merge request is being backported and why

The MR backports the fix for classic duo chat being stuck in loading after a response is received to 18.6-stable-ee

Original MR: !213292 (merged)

Original issue: #581270 (closed)

Request to backport: #581270 (comment 2939044399)

Before	After
2025-12-10-11-15_before.webm	2025-12-10-11-22_after.webm

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• This MR is backporting a bug fix, documentation update, or spec fix, previously merged in the default branch.
• The MR that fixed the bug on the default branch has been deployed to GitLab.com (not applicable for documentation or spec changes).
• The MR title is descriptive (e.g. "Backport of 'title of default branch MR'"). This is important, since the title will be copied to the patch blog post.
• Required labels have been applied to this merge request
  • severity label and bug subtype labels (if applicable)
  • If this MR fixes a bug that affects customers, the customer label has been applied.
• This MR has been approved by a maintainer (only one approval is required).
• Ensure the e2e:test-on-omnibus-ee job has succeeded, or if it has failed, investigate the failures. If you determine the failures are unrelated, you may proceed. If you need assistance investigating, reach out to a Software Engineer in Test in #s_developer_experience.

Note to the merge request author and maintainer

If you have questions about the patch release process, please:

• Refer to the patch release runbook for engineers and maintainers for guidance.
• Ask questions on the #releases Slack channel (internal only).
• Once the backport has been merged, the commit changes will be automatically deployed to a release environment that can be used for manual validation. See after merging runbook for details.