Inconsistent workspace access display after user removal

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**Description**
When a user is removed from a workspace but is still logged in to the QGIS plugin, there's an inconsistency in how workspace membership is displayed. The plugin shows a warning that the user doesn't have any workspace available, but in the browser panel, the user still appears as a member of that workspace. This creates a confusing user experience as the information presented is contradictory.

**Environment**
Staging

**Application (+ app version, build, operating system)**
- QGIS version: 3.40.5-Bratislava
- Plugin version: 2025.1.1
- OS: macOS, Sequoia 15.5

**Steps to reproduce**
1. Log in to the MerginMaps QGIS plugin with a user account that has access to a workspace
2. Have an administrator remove the user from the workspace (kick the user off)
3. While still logged in to the QGIS plugin, refresh the workspace
4. Observe the warnings and browser panel

**Actual results**
- The plugin shows a warning that the user doesn't have any workspace available
- In the browser panel, the user still appears as a member of the workspace they were removed from

**Expected results**
- The browser panel should reflect the current workspace permissions and not show workspaces the user no longer has access to
- The information displayed in warnings and the browser panel should be consistent

**Screenshots or logs**


*Conclusion*
*Created by GitHub Copilot and supervised by a human test analyst.*

Reproduce the removal and refresh sequence in the QGIS plugin, then trace how workspace refreshes update the warning and browser panel membership display. Done means both views consistently reflect the user's current workspace permissions and no longer show the removed workspace.

Written by the indexing model from the issue text.