Copilot not processing chat queries

### Description

Not processing chat queries with MSSQL and Copilot. It continues to ask for a connection or takes long to process queries and it times out

### Steps to Reproduce

1. Installed the MSSQL extension
2. Connect to DB
3. Opened my database with Copilot mode
4. Run a query
5. Message stating no connection found
6. Follow the Connect to the Database button/prompt
7. Successfully connect to the database instance
8. Run query again
9. Expected: run multiple back to back prompts against the database
10. Actual: Queries are timing out. Or the first query is processed but any follow up queries trigger the same "not connected" message.

### Affected Area

- [x] Agent mode
- [x] Ask mode
- [ ] Slash commands
- [ ] Code generation
- [ ] Connection management
- [ ] Schema exploration and object management
- [ ] Query execution and performance advisor
- [ ] Other (please describe below)

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

_No response_

### Environment Information (Optional)

VS Version: 1.110.0-insider
MSSQL Version: 1.40.0
GitHub Copilot Version 0.39.2026030404
OS: Tahoe 26.2
Connection Type: SQL Server (Migrated from Azure Data Studio)

### Confirmation

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