What

Makes the skill-discovery image emit the two pieces a SEP-2640-aware MCP client needs to enumerate skills without fetching every SKILL.md:

1. skill://index.json resource — an Agent Skills discovery index built from the in-memory skill set. Each entry: { "type": "skill-md", "name", "description", "url": "skill://github/<name>/SKILL.md", "allowedTools": [...] }. $schema = https://schemas.agentskills.io/discovery/0.2.0/index.json.
2. io.modelcontextprotocol/skills capability extension — advertised in the initialize result so clients opt into skill:// discovery.

Stacked on sammorrowdrums/skills-over-mcp-refactor (#2374). The branch already registers per-skill skill://github/<name>/SKILL.md resources and parses allowed-tools frontmatter; this PR exposes that same data through the well-known index + the capability flag.

Why

The skills-over-mcp-refactor branch lists skills only as individual resources/list entries, with allowed-tools buried inside each SKILL.md, and advertises no skills extension. A SEP-2640 client that gates on the extension + reads skill://index.json therefore discovers zero skills from the image. This PR closes that gap so the discovery index and the per-skill allow-lists are available up front, enabling clients to defer a skill's tools until the skill is loaded.

Implementation notes

• Only the Extensions field is set on ServerOptions.Capabilities; the Go SDK still infers tools/resources/prompts from registered handlers (Server.capabilities() only fills nil fields), so advertising the extension does not clobber the existing capabilities.
• The index reuses allSkills() / each skill's allowedTools — no new source of truth.

Tests

• TestBuildSkillIndex / TestBuildSkillIndexJSON_IsValid — index shape: one skill-md entry per skill, correct url, non-empty allowedTools, valid JSON.
• TestSkillsExtensionAndIndexAdvertised — end-to-end in-memory initialize: the skills extension is advertised (and tools/resources are still present), and skill://index.json serves the discovery shape.
• gofmt, go vet, and the full pkg/github suite pass.

Verified against a SEP-2640 consumer

Built the binary from this branch and ran a real client discovery loop:

extensions advertised: {"io.modelcontextprotocol/skills":{}}
Discovered 27 skill(s) over MCP from server "github": get-context, explore-repo, ...
skills carrying allowedTools (deferral-ready): 27 / 27

Co-authored-by: Copilot 223556219+Copilot@users.noreply.github.com