Follow-up to the cherry-picked #111876 (@KoNit-K), which shares the design
of the earlier #111875 by the issue author (@ats3v): emit DeepInfra's
top-level ``reasoning_effort`` from the provider profile, ungated on
``supports_reasoning``, ``none`` as the only off switch, ``xhigh`` native,
``ultra`` clamped to ``max`` via the shared vocabulary, unset/unknown omitted.
- drop the constructor/blank-line reformat churn (byte-identical to main)
- replace the 14-case test file with two invariant tests: the profile's
config -> top-level field table, and the transport main-turn path with
``supports_reasoning=False`` (the gate the core allowlist actually passes)
- docs: DeepInfra subsection in integrations/providers.md describing the
two-directional reasoning control
Offline kwargs probe: before every reasoning_config -> ({}, {}) and the
main turn carried no reasoning field; after ``high`` -> ``reasoning_effort:
high``, ``{'enabled': False}`` -> ``none``, ``ultra`` -> ``max``, unset and
unknown levels omitted, aux calls stop emitting the generic
``extra_body.reasoning`` for this provider.
Co-authored-by: Georgi Atsev <georgi@deepinfra.com>
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