## Summary

The audio panel's OUTPUT slider and its mute toggles have no effect on real
loudness. The percentage, the knob and the OSD all move; the audio does not.
Per-application sliders (SOURCES) work correctly.

Volume keys (`omarchy-audio-output-volume`, via `pactl`) also work correctly,
which makes the panel look like the odd one out.

## Cause

`plugins/panels/audio/Panel.qml` writes volume to the *node*:

```qml
volumeSink.audio.volume = volume       // setOutputVolume
volumeSink.audio.muted = ...           // toggleOutputMute / toggleAllMuted
source.audio.volume = ...              // setInputVolume
```

On a **device** sink that write is cosmetic. It updates the node's
`channelVolumes`, but the applied gain (`softVolumes`) never moves, so nothing
gets attenuated. Loudness on a device sink lives on its route, which is what
`pactl` and `wpctl` set.

Stream nodes are unaffected and take a direct node write, which is exactly why
the per-app sliders work and the output slider does not.

## Reproduction

Any device sink (reproduced on both a Bluetooth A2DP sink and an ALSA one):

```console
$ pw-dump 43 | jq '.[].info.params.Props[] | {channelVolumes, softVolumes}'
{ "channelVolumes": [0.216, 0.216], "softVolumes": [0.216, 0.216] }

# node-Props write -- what the panel does
$ pw-cli s 43 Props '{ channelVolumes: [ 0.05, 0.05 ] }'
$ pw-dump 43 | jq '.[].info.params.Props[] | {channelVolumes, softVolumes}'
{ "channelVolumes": [0.05, 0.05], "softVolumes": [0.216, 0.216] }   # gain unchanged
$ pactl get-sink-volume <sink> | head -1
Volume: front-left: 39322 / 60% ...                                 # still 60%

# route write -- what pactl/wpctl/the volume keys do
$ wpctl set-volume 43 0.30
$ pw-dump 43 | jq '.[].info.params.Props[] | {channelVolumes, softVolumes}'
{ "channelVolumes": [0.027, 0.027], "softVolumes": [0.027, 0.027] } # gain follows
```

Mute splits the same way: `pw-cli s 43 Props '{ mute: true }'` yields node
`mute=True` with `softMute=False`, and `pactl get-sink-mute` still reports
`Mute: no`.

## Fix

Route the device-node writes through `pactl`, the way the volume keys already
do, and leave the stream-node writes alone. Patched locally in
`setOutputVolume`, `setInputVolume`, `toggleOutputMute`, `toggleInputMute` and
`toggleAllMuted`:

```qml
function writeOutputVolume(volume) {
  if (!volumeSink) return
  Quickshell.execDetached(["pactl", "set-sink-volume", String(volumeSink.name),
                           Math.round(volume * 100) + "%"])
}
```

A drag emits a move per mouse event and each write is a process, so the output
write is gated at 40 ms: the first goes out immediately, and any arriving
during the window are coalesced into one at the end of it.

Reads need no change -- a route write updates `channelVolumes` too, so the
panel's displayed value stays correct.

## Environment

- omarchy 4.0.0.alpha
- quickshell 0.3.1-1
- wireplumber 0.5.15-1
- pipewire 1:1.6.8-1