Microphone sporadically fails to record after connecting Bluetooth headphones (0.7.6)

**Describe the bug**
On Hex 0.7.6, the microphone sporadically fails to record after I connect Bluetooth headphones on macOS. Most of the time Hex records fine, but after some audio route changes (especially when Bluetooth headphones are connected as the output), some recordings produce no transcription as if no audio was captured, even though the recording UI appears as normal. Both Accessibility and Input Monitoring permissions are enabled for Hex.

**To Reproduce**
Steps to reproduce the behavior:

1. Launch Hex 0.7.6 on macOS Tahoe 26.5.1 (25F80).
2. In System Settings → Privacy & Security, ensure Hex has both Accessibility and Input Monitoring permissions.
3. Use Hex normally with your hotkey (e.g. press-and-hold to record, or double tap to lock), and verify it records and transcribes correctly (internal mic)
4. Connect a Bluetooth headset
5. Continue using Hex with the same input device and hotkey.
6. Now some hotkey presses will:
- Show the usual Hex recording UI, but no mic icon appears in menu bar
- Only after a few times pressing, the Mic icon appears
- But sporadically produce no audio/transcription (other presses in the same session still work).

**Expected behavior**
- Hex should continue to record from the selected input device (internal mic or USB mic) even when I connect or disconnect Bluetooth headphones as the output device.
- Every hotkey-triggered recording should consistently capture audio and produce a transcription, regardless of audio route changes.

**Screenshots**
N/A (no visual error; the issue is that some recordings silently produce no transcription).

**Desktop (please complete the following information):**
- macOS version: macOS Tahoe 26.5.1 (25F80)
- Mac model: MacBook Pro 16-inch, 2023, Apple M2 Max, 32 GB RAM
- Hex version: 0.7.6
- Input devices used:
- Built-in microphone
- [Optional] USB audio interface (e.g. Scarlett)
- Output devices used:
- Internal speakers
- Bluetooth headphones (output only; I do not intend to use their mic)

**Additional context**
- The problem is intermittent: most recordings work, but after connecting Bluetooth headphones the mic occasionally fails to capture audio until I press recording a few times. It feels like i need to "nudge" the mic a few times
- Both Accessibility and Input Monitoring remain enabled at all times.
- This behavior occurs while using the hotkey (single + double tap);
- This may be related to recent audio changes around route changes and to the known issue about Bluetooth headset mics failing when switching between A2DP and other profiles.

Start by tracing the legacy Swift macOS app's hotkey-triggered recording path and its handling of microphone input when Bluetooth output routes change. Reproduce the intermittent failure using the listed internal or USB microphones and Bluetooth headphones, then verify that every recording captures audio and produces a transcription after route changes.

Written by the indexing model from the issue text.