docs(api): align documentation with v2 API structure and terms

[seanbrar]

Summary

Aligns the user-facing documentation with the Pollux v2 API architecture and terminology, replacing deprecated parameters (e.g. Options, response_schema, continue_from, continue_tool) with their v2 equivalents (Environment, output, continuation, interact, stream).

Related issue

None

Test plan

Non-behavioral change (documentation updates). Verified that:

• just lint (Ruff formatting, ruff check, rumdl link checks) runs and passes cleanly.
• just docs-build (MkDocs compilation) builds successfully without warnings.
• just typecheck and just test run successfully to confirm no regressions.

Notes

All documentation files have also been audited against internal styling guidelines.

---

• PR title follows conventional commits
• just check passes
• Tests cover the meaningful cases, not just the happy path
• Docs updated (if this changes public API or user-facing behavior)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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