[Bug]: Improve SQL Notebooks quality and performance

### Description

NPS feedback ahead of GA surfaced several quality and performance issues with SQL Notebooks that need to be addressed before release.

**Issues reported from NPS:**
* Runtime instability: Kernel intermittently switches from MSSQL to Python, and results don't always render correctly.
* Unclear connection state: Noticeable lag when connecting via notebook with no clear indicator of connection status (standard queries are fine).
* Errors not surfaced: Failed queries in notebooks don't show error messages.
* Weak IntelliSense: Completions/suggestions in notebook cells are not helpful.

**Proposed fixes:**
* Kernel stays on MSSQL and does not switch unexpectedly
* Results render reliably across cells
* Clear connection state indicator; notebook connection latency on par with standard editor
* Query errors surfaced in cell output
* IntelliSense reaches parity with the standard SQL editor

### Steps to Reproduce

1. Open the MSSQL extension
2. Connect to a database
3. Create a new SQL Notebook

### 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
- [ ] SQL Database projects
- [ ] Query Plan Visualizer
- [x] Other (please describe below)

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

SQL Notebooks

### Environment Information

- VS Code: Latest
- MSSQL extension: Latest

### Confirmation

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

Start by reproducing the SQL Notebook flow described in the three steps, using the listed MSSQL environment. Investigate each reported symptom—kernel switching, result rendering, connection status, query errors, and IntelliSense—and consider the work done only when the proposed notebook behavior matches the standard SQL editor where specified.

Written by the indexing model from the issue text.