refactor(core): promote mot._thinking to public mot.thinking #1217

Sub-issue of #909. Design discussed in #1197 Area 4.

Summary

_thinking is documented as private (single underscore) but referenced publicly in docs/docs/integrations/openai.md:

If you intend to use thinking mode, read the reasoning trace from result._thinking rather than result.value.

Promote to mot.thinking; keep _thinking as a deprecated alias for one minor release.

Design

• Rename the attribute to mot.thinking (no leading underscore).
• Add a _thinking property that returns self.thinking and emits DeprecationWarning on read.
• Backends keep populating through the public name.
• Update docs/docs/integrations/openai.md to reference result.thinking in the same PR.

Considered alternatives (rejected)

• mot.generation.thinking — matches the "execution metadata" flavor of usage and finish_reasons. Rejected: reasoning is content the model produced, semantically closer to value than to usage; longer dotted path for content most users want directly.
• mot.reasoning.* namespace — would give room for future structured reasoning data. Rejected as speculative: reasoning is currently a flat string across all backends. mot.thinking doesn't preclude introducing mot.reasoning.* later.

Deprecation horizon

One minor cycle, then remove (OQ3 resolution). Pre-1.0 + the only published reference is in our own docs (updated in this PR). One minor with DeprecationWarning is sufficient.

Related: #1201

Promoting mot.thinking to public is only half the story — Message has no thinking field and chat.py:_parse ignores _thinking entirely, so reasoning is silently dropped in multi-turn chat. #1201 tracks the Message-level fix. Both should ship together if possible (so a freshly-public mot.thinking actually round-trips through chat history), but #1201 is independent and can ship later if needed.

Appendix items folded in

From #1197's Appendix A:

• Item 9 — docs/docs/integrations/openai.md instructs users to read result._thinking. Update to result.thinking in this PR.

Acceptance

• mot.thinking is the public attribute; backends write through the public name
• mot._thinking is a deprecation-warning shim
• docs/docs/integrations/openai.md updated
• Existing tests unchanged in behavior
• Release notes / changelog entry calling out the deprecation horizon
• Better handling of reasoning output from thinking models #1201 cross-referenced

Sequencing

Independent of Area 1 (#1215), Area 3 (#1216), Area 5 (#1191) and of #1181. Can ship in any order.