docs: deterministic API reference + docs-check CI gate (Phase A)

[moonyue-w]

What

Phase A of the SDK repository-management effort: a documentation gate for the TS SDK. No release signing, no examples-smoke (deferred), no runtime changes.

1. Deterministic API reference generation (make docs / npm run docs) via TypeDoc + typedoc-plugin-markdown, reading public exports + JSDoc into committed docs/api/.
2. A docs-check gate (make docs-check / npm run docs:check) that regenerates and fails on drift, checks internal links, and compiles README ts snippets.
3. A docs-check CI job wired into ci.yml (Node 22.x), runnable as a required PR check. The existing test matrix and permissions are unchanged.

Verification

• make docs re-generation byte-identical (deterministic); no timestamps/abs-paths/host info.
• npm run docs:check: PASS on clean tree; JSDoc drift → non-zero (reverse-verified).
• Full suite: 3333/3333 pass.
• Clean-room reproduction (fresh clone + npm ci + build + docs:check on Node 22.x): PASS.

Scope / out of scope

• Deferred: examples-smoke + examples/tests decoupling (tracked separately) due to a circular examples↔tests dependency.
• Remote branch-protection / required-checks config is documented, not applied here.