Capture engine records silence from all local (non-Bluetooth) input devices — only AirPods work

**Environment:** Hex (latest, 0.8.x) · macOS 26.x · Apple Silicon · Model: Parakeet TDT v2

**Summary:**
Hex records digital silence from every wired/built-in input device I have. The full
pipeline runs (engine arms, buffers are produced, Parakeet transcribes) but the audio is
empty. The ONLY device that works is AirPods. macOS's own Sound → Input meter shows all
these mics working, and other apps capture them fine, so the mics/permissions/hardware are
not the issue.

**Devices tested:**
| Device | Format | Result |
|---|---|---|
| AirPods Pro 1 (BT) | 24 kHz, 1ch | ✅ works |
| AirPods Pro 2 (BT) | 48 kHz, 2ch | ✅ works |
| Built-in MacBook mic | 48 kHz, 1ch | ❌ silence |
| Samson Q2U (USB) | 48 kHz, 2ch | ❌ silence |
| Samson Q2U (USB) | 16 kHz, 1... (Hz forced) | ❌ silence |

**Ruled out (each tested):**
- Sample rate — AirPods Pro 2 is 48 kHz and works; Samson forced to 16 kHz still fails.
- Channel count — AirPods Pro 2 is 2ch and works; built-in is 1ch and fails.
- Permission — AirPods working proves Hex holds mic/TCC access.
- Super Fast mode — fails identically ON and OFF.
- Device (re)selection, changing macOS default input, and USB replug/rebind — no effect.

**Common factor:** the only working devices are Bluetooth headsets that are a single device
for BOTH input and output. Every input-only device (built-in mic, USB mic) — where input ≠
the output device (built-in speakers) — records silence. Log shows a
`CADefaultDeviceAggregate-…` bound to `BuiltInSpeakerDevice` in the failing case.

**Log evidence (failing, Samson selected):**
[Recording] Capture engine first buffer … frames=1632
[Parakeet] clip check … channels=1
[Transcription] Transcribed audio … to text length 0
(`frames=1632` appears to be only the silent pre-roll; no live audio is captured.)

**Suspected area:** `SuperFastCaptureController` — the `AVAudioConverter(from: inputFormat,
to: 16kHz)` path and/or `AVAudioEngine.inputNode` binding when the input device differs from
the output device (the OS builds a CADefaultDeviceAggregate that yields silent input buffers).

**Related:** #204 (multichannel Scarlett records silence), #251 (output device breaks built-in
mic input), #218, #252, #264.

Start in SuperFastCaptureController, focusing on the AVAudioEngine.inputNode binding and AVAudioConverter path when the selected input differs from the output device. Reproduce with the built-in mic or Samson Q2U, compare logs and buffers against AirPods, and verify that non-Bluetooth devices produce live audio rather than only silent pre-roll frames.

Written by the indexing model from the issue text.