[Feature Request]: Ability to restrict which connections are available to Copilot

### Feature Description

Please add an explicit flag in the connection settings to control whether this connection is allowed to be used by agents via MCP.

### Problem and Motivation

I have many saved connections, including connections to sensitive databases. I have an instruction for Copilot that describes which connections are allowed, but there is always a risk that it may ignore it.

### Related Area

- [x] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [ ] Query editor
- [ ] Query results panel
- [ ] Object Explorer
- [x] 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
- [x] I want to help implement this feature

Start by tracing the connection dialog and GitHub Copilot integration identified in the issue, including how MCP agents access saved connections. Define how the setting is represented and enforced; done means a connection can be explicitly excluded from agent use while remaining available elsewhere.

Written by the indexing model from the issue text.