[Feature Request]: connection-sharing capability

### Feature Description

continue to support current connection-sharing capability.

### Problem and Motivation

I use it on my own extension to query SQL Server without the all hassle of connections, password, etc.

### Related 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
- [ ] 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