[Bug]: Disconnection from databases due to inactivity

### Description

The databases disconnect after a few hours, but they don't show up as disconnected. The error occurs because it doesn't allow you to update stored procedures, tables, etc.; it just stays in the “loading” state.

### Steps to Reproduce

1. Connect to an SQL database server that contains more than one database
2. Execute stored procedures while switching between databases
3. Leave Visual Studio Code idle for several hours
4. Try to update tables or stored procedures
5. When attempting to disconnect, it won't let you disconnect either

### Affected Area

- [ ] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [ ] Query editor
- [ ] Query results panel
- [ ] 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
- [x] SQL Database projects
- [ ] Query Plan Visualizer
- [ ] Other (please describe below)

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

_No response_

### Environment Information

SQL Server (mssql) vcersion 1.41.0

### Confirmation

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