feat(api): add Session runtime and provider readiness probes

[seanbrar]

Summary

Make multi-turn agent loops first-class without re-creating a provider per call.

• Session owns one provider instance across many interact() / stream() / run_many() turns and closes it on exit. The one-shot module helpers now delegate to a single-use Session, so their behavior is unchanged.
• Readiness probes: a ReadinessProvider protocol + ProviderReadiness result let a provider expose a fast preflight. Session.check_ready() and the module-level check_ready() probe before packing context. The local provider implements it against /health and /v1/models, verifying the configured model when one is set.
• local_reasoning() helper returns the scoped provider_options for local servers that honor enable_thinking.

Related issue

None

Test plan

just check passes (ruff format, ruff check, mypy, 443 tests). New tests:

• tests/interaction/test_interact_frontdoor.py: Session reuses and closes its provider; module-level check_ready() uses the provider probe; local_reasoning() shape.
• tests/providers/test_local_contract.py: local check_ready health-endpoint path, models fallback, missing-model reporting, model-unset skip, and model-verification requirement.

Notes

Third and final PR in the v2 RC stack. Stacked on #213 (which is on #212).

---

• 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

❌ Patch coverage is 77.04918% with 14 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/pollux/providers/local.py	73.46%	13 Missing ⚠️
src/pollux/providers/base.py	91.66%	1 Missing ⚠️

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