Mentions not updated simultaneously in the sidebar when a new member is added

Description:

When a new mention is added to the chat, the mentions list in the sidebar does not update immediately. The new mention only appears after refreshing the page.

Steps to reproduce:

1. Mention someone in the chat
2. Observe that the new mention does not appear in the mention sidebar immediately.
3. Refresh the page and observe that the new mention now appears in the members sidebar.

Expected behavior:

Mention should be updated simultaneously.

Actual behavior:

https://github.com/user-attachments/assets/da117c55-33c7-47b8-a531-256ac177a238

Server Setup Information:

• Version of Rocket.Chat Server: 7.3.2
• License Type:
• Number of Users: 2
• Operating System: macOS
• Deployment Method: meteor
• Number of Running Instances: 1
• DB Replicaset Oplog: Enabled
• NodeJS Version: 22.11.0
• MongoDB Version:7.0.5

Client Setup Information

• Desktop App or Browser Version: browser
• Operating System: macOS

Additional context

Relevant logs:

Reproduce the issue in the browser by adding a mention and observing the sidebar before and after a refresh. Trace the frontend entry point responsible for the mentions sidebar and its update flow; done means a newly added mention appears immediately without a page refresh, with a regression test if the project provides one.