SDK/TUI: add high-level parity coverage, documentation, and examples

Parent story: #1466

Goal

Make high-level SDK coverage intentional and regression-resistant, and document which mecatui behaviors belong in the SDK versus the application or operator layer.

Scope

• Inventory every public RPC and classify it as a Session method, SDK namespace operation, lifecycle object, or intentionally raw-only operation.
• Inventory every mecatui builtin and classify it as SDK-backed, application/presentation-only, operator/configuration-only, or debug-only.
• Record a short rationale for every intentionally raw-only RPC and every builtin that should not become an SDK API.
• Add a high-level surface coverage test in addition to the existing raw RPC reachability/parity check.
• Update generated/public API reports for intentional surface changes.
• Add user documentation and runnable examples for the session lifecycle, capability discovery, MCP enrollment, and MCP authorization workflows delivered by the sibling sub-issues.
• Update the TypeScript SDK changelog and any relevant living architecture documentation.

Boundaries

• Coverage does not mean one SDK method per RPC or one SDK method per TUI command.
• Do not expose presentation-only actions such as help, quit, overlays, filtering, keybindings, clipboard behavior, or debug prompts.
• Do not move local provider configuration, credential management, or TUI preference persistence into the SDK.

Acceptance criteria

• The RPC and TUI-builtin classifications are checked in and leave no unclassified entries.
• CI fails when a new public RPC or builtin is added without an explicit high-level-surface classification.
• The coverage mechanism distinguishes raw transport reachability from ergonomic high-level coverage.
• Documentation explains the authority boundary: server logic, SDK protocol choreography, and application presentation/policy.
• Examples compile/run under the repository's normal SDK verification workflow.
• Public API reports and changelog entries match the shipped SDK surface.

Start with the existing raw RPC reachability/parity check and the TypeScript SDK verification workflow. Inventory the public RPCs and mecatui builtins, record classifications and rationales, then define the high-level coverage check alongside the requested documentation and runnable examples. Done means no unclassified entries, coverage distinguishes raw from ergonomic APIs, and reports and changelog match the shipped surface.