Is your feature request related to a problem? Please describe.

Users have no guidance on using ${input:...} variables in MCP server headers and env fields. The documentation at IDE & Tool Integration — MCP Server Declaration and the Manifest Schema reference don't mention this capability.

Depends on #342.

Describe the solution you'd like

Document ${input:...} variable support in the following pages:

1. docs/src/content/docs/integrations/ide-tool-integration.md — MCP Server Declaration section: add a subsection explaining ${input:...} syntax in headers and env, with a practical example.

2. docs/src/content/docs/reference/manifest-schema.md — headers and env field descriptions: note that values can contain ${input:<id>} references for VS Code runtime prompting.

Content to include

• ${input:...} syntax — values in headers and env can reference VS Code input variables using ${input:<variable-id>}.

• How it works — for registry-backed servers, APM auto-generates input prompts from registry metadata. For self-defined servers, APM detects the patterns and generates matching definitions.

• Runtime support matrix:

  Runtime	${input:...} support
  VS Code	Yes — prompts user at runtime
  Copilot CLI	No — use environment variables
  Codex	No — use environment variables

• Examples:

  dependencies:
    mcp:
      - name: my-server
        registry: false
        transport: http
        url: https://my-server.example.com/mcp/
        headers:
          Authorization: "Bearer ${input:my-server-token}"
          X-Project: "${input:my-server-project}"

Describe alternatives you've considered

Leaving it undocumented, but this leads to user confusion (as evidenced by genuine questions about the feature).

Additional context

Keep documentation concise and task-oriented per project conventions. This should be a short subsection, not a separate page.