feat: trace inline <think> reasoning and time thinking tokens

[milanagm]

Summary

• Carries the two parts of feat: trace reasoning content and offered tools on generations #37 (by @Ali-Aleph-Alpha) that are genuinely still missing on main. The rest of that PR had already landed independently while it was open: the reasoning-on-output half via feat: carry assistant reasoning on the generation output too #38 (merged 2.5 h after feat: trace reasoning content and offered tools on generations #37 was opened) and the tool definitions via feat: attach the offered tool definitions to every generation #34.
• Inline <think> reasoning. pi turns a provider's structured reasoning_content delta into a thinking part, but some OpenAI-compatible servers stream the reasoning inline as <think> tags in the text content instead — the vLLM default, the DeepSeek distills, and proxies in front of either. pi keeps that text verbatim (pi@0.84.2 has no occurrence of <think> anywhere in dist), so the reasoning was traced as the answer. splitInlineThinking / extractAnswerAndThinking now split it out and feed it through the existing extractThinking, so inline reasoning travels the same path as structured reasoning. Only a leading tag counts, which keeps an answer that merely mentions a <think> tag — a coding agent explaining one — from being rewritten. Structured parts win, so a model emitting both is not traced twice.
• Time to first token counts thinking tokens. message_update only set completionStartTime on non-empty extractText(...). A reasoning model streams its thinking before any answer text, so a generation that reasons and then calls a tool without prose got no TTFT at all, and a reason-then-text one reported TTFT ≈ the whole call duration. It now also checks extractThinking(...).

Linear: https://linear.app/clickhouse/issue/LFE-16443/pi-plugin-inline-think-reasoning-is-traced-as-the-answer-and-thinking
Fixes LFE-16443

Verification

• 133/133 tests + typecheck clean. Both new integration tests fail against main's src/index.ts (verified by stashing only that file), so they pin the actual gaps rather than the new code.
• New coverage: leading-tag split, an answer that only talks about the tag, structured-over-inline precedence, an end-to-end [inline-think] mock run, and a deterministic [think-tool] run asserting that a thinking-only generation reports a TTFT.
• Real Anthropic reasoning model (haiku-4-5, --model claude-haiku-4-5:medium), same script and prompts both sides, read back via /api/public/v2/observations:
  • before — https://cloud.langfuse.com/project/cmt01ylzj016zad0ek3bokien/traces/dd73c7110cf9d7c2fa90be567c361714 — of 4 generations, 2 report no TTFT at all; the other two 1.147 s of 1.254 s (91 %) and 0.953 s of 0.975 s (98 %)
  • after — https://cloud.langfuse.com/project/cmt01ylzj016zad0ek3bokien/traces/74ba2de5b034fe1a67b6b546b22756cb — the thinking-only generations report 0.744 s and 0.586 s; the text ones 37 % and 75 % of latency
• Inline <think> end to end against the mock provider: before — https://cloud.langfuse.com/project/cmt01ylzj016zad0ek3bokien/traces/128ec626e57b7b87ee6c8833db83ada1 (no thinking, raw <think> inside content); after — https://cloud.langfuse.com/project/cmt01ylzj016zad0ek3bokien/traces/ee29b23254651afcac144e2ca3d13eb7 (reasoning in its own block, <think> in no span).
• That shape is not exotic: across the 14 real pi session transcripts in ~/.pi/agent/sessions, 39 of 77 assistant messages carry structured thinking and 6 of those have no text part at all.

Why this is a draft

The inline-<think> split emits {type: "thinking", content}, and that shape currently does not render in the Langfuse trace preview — a regression in the normalized I/O parser, filed as LFE-16438 / langfuse/langfuse#17610. The payload here is correct either way, and TTFT renders today, but the reasoning block only becomes visible once that upstream fix deploys. Keeping this a draft until then so the end-to-end check can be done in the UI rather than only against the API.

Not in this change

• README.md is untouched, so the feature list still says only "each thinking block is on the step that made it" — worth a follow-up sentence once the upstream render fix is out.
• feat: trace reasoning content and offered tools on generations #37's available_tools half is deliberately dropped: feat: attach the offered tool definitions to every generation #34 already attaches tool definitions to the generation input, which is both what the UI renders and what the SDK's mask covers. feat: trace reasoning content and offered tools on generations #37 put them in metadata, which is flattened per key before export and therefore never masked.
• feat: trace reasoning content and offered tools on generations #37's readAvailableTools falls back to all registered tools when getActiveTools() returns [], which inverts that PR's own "tool not offered vs not chosen" goal. Not carried over.
• A generation that streams only a tool call, with neither thinking nor text, still reports no TTFT. There is no token to time there; timing the first tool-call delta would be a separate change.