refactor(audio): extract DeviceSetup + shared rate-match helpers (phase 4)

Moves probeDeviceOptionsDual, applyDuplexSetup, applySplitSetup, and
teardownSplitMode verbatim into src/audio/engine/DeviceSetup.{h,cpp}. The
component holds references to the two device managers + EngineState and owns
no lifetime; engine-owned collaborators (monitor chain, split output ring +
counters, output callback registration) are passed by reference per call.
setAudioDevices stays on the facade as the orchestrator. The public
DeviceOptions/DeviceConfig/DeviceConfigResult shapes move to the slopsmith
namespace with using-aliases on AudioEngine, so the NodeAddon spelling is
unchanged.

Lands the deep-read §7 dedupe structurally: the <=0.5 rate tolerance,
midpoint-rounding fail-closed candidate, and empty-name→first-enumerated
resolution now exist once (RateMatch.h — JUCE-free + unit-tested boundary
cases — and DeviceSetup::resolveDeviceName/rateSupportedBy) instead of three
hand-synced copies.

Full device-matrix validation (WASAPI shared/exclusive, ASIO, dual-type
split) rides the next tester build per the plan's phase-4 gate.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/engine_units/CMakeLists.txt

@@ -20,3 +20,7 @@ add_test(NAME engine_state COMMAND engine_state_test)
 add_executable(renderer_bus_test renderer_bus_test.cpp)
 target_compile_features(renderer_bus_test PRIVATE cxx_std_20)
 add_test(NAME renderer_bus COMMAND renderer_bus_test)
+
+add_executable(rate_match_test rate_match_test.cpp)
+target_compile_features(rate_match_test PRIVATE cxx_std_17)
+add_test(NAME rate_match COMMAND rate_match_test)

tests/engine_units/rate_match_test.cpp

@@ -0,0 +1,46 @@
+// Phase 4 unit tests (docs/audio-engine-tlc.md §5): the rate-tolerance and
+// midpoint-rounding boundary cases the three previously hand-synced sites in
+// AudioEngine.cpp narrated in comments, now pinned against the one shared
+// implementation in engine/RateMatch.h.
+
+#include "../../src/audio/engine/RateMatch.h"
+
+#include <cassert>
+#include <cstdio>
+
+using slopsmith::ratesMatch;
+using slopsmith::nominalRateCandidate;
+
+int main()
+{
+    // Tolerance is <= 0.5 (not <): a backend reporting 47999.5 against a
+    // 48000 nominal sits exactly on the boundary and MUST pass — the probe
+    // accepted it, so preflight and post-open verify must too.
+    assert(ratesMatch(47999.5, 48000.0));
+    assert(ratesMatch(48000.0, 47999.5));
+    assert(ratesMatch(48000.0, 48000.0));
+    assert(!ratesMatch(47999.4, 48000.0));   // 0.6 apart → reject
+    assert(!ratesMatch(44100.0, 48000.0));
+
+    double c = 0.0;
+
+    // Exact pair → exact nominal.
+    assert(nominalRateCandidate(48000.0, 48000.0, c) && c == 48000.0);
+
+    // Fractional drift on both sides rounds to the clean nominal.
+    assert(nominalRateCandidate(47999.5, 48000.0, c) && c == 48000.0);
+    assert(nominalRateCandidate(48000.4, 48000.1, c) && c == 48000.0);
+
+    // Fail-closed midpoint case from the original comment: 48000.4/48000.6
+    // passes the pair check (diff 0.2) but rounds to 48001 (midpoint 48000.5
+    // rounds up), which is 0.6 from 48000.4 — outside tolerance of one side,
+    // so no candidate is surfaced.
+    const bool ok = nominalRateCandidate(48000.4, 48000.6, c);
+    assert(!ok && "midpoint-rounding must stay fail-closed");
+
+    // Non-matching pair → no candidate at all.
+    assert(!nominalRateCandidate(44100.0, 48000.0, c));
+
+    std::puts("rate_match: all cases passed");
+    return 0;
+}