fix(ai): fit thinking budgets to the output limit - #51157

Issue for this PR

N/A. Found while testing default output limits for #51021.

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Protocols that send an explicit thinking budget now cap it at half the output limit. Thinking counts against the output limit, so a budget near or above it leaves the answer, a tool call or a summary with no room.

ProviderShared.fitThinkingBudget is the single rule:

• a budget at or under half the limit passes through unchanged;
• special values such as Gemini's -1 (dynamic) and 0 (off) pass through;
• requests without an output limit pass through;
• the result never goes below a provider's minimum.

It applies in the four protocols that read a typed budget:

Main steps are mostly unaffected, because variant budgets are usually at most half the model's output limit. The cap applies to compaction summaries (32k), near-full contexts, and budgets derived from the whole output limit.

Not covered:

• OpenRouter passes reasoning through untyped.
• Bedrock Converse and NVIDIA receive budgets as raw body fields that are merged after the protocol runs.

How did you verify your code works?

• Unit tests: fit tests for Anthropic (including the minimum), Alibaba Chat and Messages, and Gemini (including -1 and the 512 minimum). The full packages/ai suite passes.

• Gemini minimums, live on AI Studio:

  Model	Rejected (400)	Accepted
  2.5 Flash-Lite	1, 500, 511: "choose a value between 512 and 24576"	512
  2.5 Pro	100, 127: "choose a value between 128 and 32768"	128
  2.5 Flash	—	1, 500

  All three accept 512 under a 1,000 limit, which is what the fit now sends there.

• Live with the default output limits from feat(core): fit output limits to the context window #51021 applied: a title, tool-using steps and a manual compaction.

  Model	Steps (limit / budget)	Compaction (limit / budget)	Before
  Alibaba qwen3.7-plus max	131,072 / 65,536	32,000 / 16,000	Answer cut after 8 tokens; compaction rejected
  Google and Vertex gemini-2.5-pro max	65,536 / 32,768	32,000 / 16,000	Budget above the summary limit
  Anthropic claude-haiku-4-5 max	64,000 / 31,999	32,000 / 16,000	31,999 under 32,000 left about one token for the summary

  All requests returned 200, and every compaction completed.

Screenshots / recordings

N/A

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR