[Feature Request]: Pin connected server / database to top of query editor

### Feature Description

I would like to always know for any open query editor, which database and server I am connected to.

### Problem and Motivation

The connection info at the top of the query editor area is excellent in preventing basic mistakes when working with multiple tabs across servers and environments.

However, when you scroll, you immediately lose this, and need to scroll to the top to see it. Ensuring that the connection info is pinned when scrolling would be ideal from a sanity checking point of view.

I am aware that you can also get this from the bottom status bar, but I find it _far_ more likely that I would have seen the bar on the tab itself.

### Related Area

- [ ] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [x] 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
- [ ] Other (please describe below)

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

_No response_

### Confirmation

- [x] I have searched existing feature requests and couldn't find a match
- [ ] I want to help implement this feature

Start at the query editor UI and trace how the connection information shown at the top is rendered and how the editor responds to scrolling. Compare it with the connection shown in the bottom status bar. Done means the server and database remain visible for each open query editor while scrolling, without changing the existing connection information.

Written by the indexing model from the issue text.