Wire get_reasoning_stale_timeout_floor() into both stale detectors so known
reasoning models (Nemotron 3 Ultra, OpenAI o1/o3, Opus 4.x thinking, DeepSeek
R1, Qwen QwQ, Grok reasoning) tolerate multi-minute thinking phases instead of
the upstream gateway idle-killing the socket (BrokenPipeError) before first
token. Applied as max(default, floor) — never overrides explicit user config,
never lowers an existing threshold.
The reasoning_timeouts.py allowlist module already landed on main via #52795,
so this salvage carries only the wiring + tests (the duplicate module and the
stale-base MoA reverts from the original PR branch are dropped).
Salvaged from #52238. Fixes#52217.
