Studio chat: browse MCP inventory and insert into a draft

Parent: #1736. Design review: #1779.
Design baseline: 2026-09-24.

Outcome

A chat user can inspect available MCP servers, tools, prompts, and resources and insert references into the composer.

Add a capability-gated MCP inventory panel and composer insert menu with clear loading, empty, error, and disconnected states.
Expose a read-only BFF projection of the published SDK's connection-scoped MCP inventory. Keep the browser behind the BFF, and keep inventory access authorized to the signed-in caller.
Use the existing draft/attachment model so insertion edits the draft without sending or executing anything.

Tools, prompts, and resources are distinguishable and searchable/browsable; choosing one inserts the intended reference at the cursor without triggering a run.
Unsupported MCP deployments show a capability explanation; anonymous requests cannot enumerate inventory.
Contract/BFF/component tests and task studio:check pass.

Bounded BFF contract addition; use the published SDK only.

Depends on: #1847, #1850.