[Bug]: Entra ID (MFA) connections prompt for sign-in twice on connect

### Description

When connecting to a saved database that uses "Microsoft Entra ID - Universal with MFA support", the extension asks me to sign in twice using the web browser.

Expected behavior: Connecting should prompt for sign-in at most once.

### Steps to Reproduce

1. In the SQL Server pane, expand a disconnected database that uses Microsoft Entra ID authentication.
2. A dialog appears saying the extension wants to sign in.
3. The Microsoft sign-in page opens in the browser; I sign in.
4. Back in VS Code, the sign-in dialog appears again.
5. The browser sign-in page opens again.
6. Only then does the connection succeed and the database contents load.

### Affected Area

- [ ] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [ ] Query editor
- [ ] Query results panel
- [x] Object Explorer
- [ ] GitHub Copilot integration
- [ ] Preview/Edit data
- [ ] Table Designer
- [ ] Schema Designer
- [ ] Schema Compare
- [ ] Local SQL Server Container provisioning
- [ ] SQL database in Fabric provisioning
- [ ] DACPAC/BACPAC export/import
- [ ] SQL Database projects
- [ ] Query Plan Visualizer
- [ ] Other (please describe below)

### If you selected "Other", please describe the affected area

_No response_

### Environment Information

- VS Code version: 1.125.1
- MSSQL Extension version: 1.43.0
- Operating system: macOS 26.4.1
- Connection type: Entra ID with MFA support

### Confirmation

- [x] I have searched existing issues and couldn't find a match
- [ ] I want to work on this issue