We are all reasonable people here, and while you are (mostly) correct, I think we can all agree that Anthropic documentation sucks. If I have to infer from the doc:

* Haiku 4.5 by default doesn't think, i.e. it has a default thinking budget of 0.

* By setting a non-zero thinking budget, Haiku 4.5 can think. My guess is that Claude Code may set this differently for different tasks, e.g. thinking for Explore, no thinking for Compact.

* This hybrid thinking is different from the adaptive thinking introduced in Opus 4.6, which when enabled, can automatically adjust the thinking level based on task difficulty.