[Ticket]: Test the MCP and A2A surfaces of LCI

### Type
Spike / Investigation

### Summary
We need to test the MCP and A2A (agent-to-agent) surfaces of Lightbridge Code Intelligence (LCI), because this sprint is about cleaning up and polishing LCI and these are two of its key integration surfaces. Expected result: both surfaces are exercised end-to-end with documented results.

### Intent
Confirm LCI's agent-facing integration points actually work as intended, not just its direct/human-facing usage.

### Source of truth (links)
Sprint planning session, 2026-07-11 (local planning doc — no public source-of-truth link yet).

### Current Behavior
TBD — needs establishing whether MCP/A2A surfaces have been tested before, and with what result.

### Expected Behavior
An MCP client can successfully call LCI's MCP tools end-to-end; an A2A-compatible agent can successfully interact with LCI via its A2A surface.

### Acceptance Criteria
- [ ] Given a real MCP client, when it connects to LCI's MCP endpoint, then it can list and invoke LCI's tools successfully.
- [ ] Given a real A2A-compatible agent, when it interacts with LCI's A2A surface, then the interaction completes successfully.
- [ ] Any failures found are documented and filed as follow-up (e.g. against the "Stabilizing LCI" ticket).
- [ ] Verification evidence is provided (see below).

### Out of Scope
Fixing issues found (tracked via "Stabilizing LCI" or new follow-up tickets).

### Technical Context
`charts/lightbridge-code-intelligence`. Check gateway MCP auth pattern (ADR-0038) if LCI's MCP surface is routed through core-gateway.

### Test Plan
TBD by ticket owner — exercise both surfaces with real clients, document pass/fail per capability.

### Verification evidence
N/A — not yet implemented. To be filled in by the ticket owner on completion.

### Human accountable owner
TBD — to be assigned during sprint planning.

### AI Usage Declaration
Drafting the ticket

### Human verification completed
(unchecked — pending assignment and human review)