[Feature Request]: Connection Group Color on Query Tab and/or Editor Connection Detail

### Feature Description

I'd like to see the connection group color be shown on the query tab. The group color on the connection in the status bar is great but kind of out of sight.

Or, if the connection detail in the upper left could be sticky and also have the group color?

### Problem and Motivation

Quick ID of what tabs are connected to my Prod/Dev groups

### 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 in the query editor area and inspect how the connection group color is currently exposed in the status bar. Compare the two requested presentation options—color on the query tab or a sticky connection detail—and define done as allowing quick identification of tabs connected to Prod or Dev groups.

Written by the indexing model from the issue text.