Merge the bridge and a home-screen interface into one app

The HEOS app is unpleasant to use for the four things that actually get
done in this house, so this is those four things on one screen: volume
for the Home 400 and the Living Room pair, joining either to the AVR,
splitting them off again, and picking the AVR's input.

The bridge's logic moves in mostly intact, split into a HEOS client, an
AVR client and a controller, with two grouping bugs fixed on the way:

  * Merging a room into the AVR sent only the pair's leader pid, which
    left the second Home 200 behind. Group targets now expand to every
    member pid, and unmerging re-forms the pair rather than leaving two
    lone speakers. The members are learned while the pair is visible and
    remembered in members.json so a restart can still rebuild it.

  * Volume for the pair used its gid, which stops existing the moment it
    joins the AVR's group. It now falls back to the member players.

Both sockets are kept open rather than reconnecting per command, which
is what made every button press feel slow; the AVR connection doubles as
a listener, so input changes made with the physical remote show up too.

The original query-string endpoints still answer, so anything already
pointed at the bridge keeps working.

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

tools/make_icons.py

@@ -0,0 +1,88 @@
+#!/usr/bin/env python3
+"""Draw the home-screen icon, with no image library to install.
+
+    python3 tools/make_icons.py
+
+Writes static/icon-180.png (what iOS uses for the home screen) and
+static/icon-512.png (Android / the web manifest). Re-run it if you want
+different colours -- they are the two constants below.
+"""
+
+import math
+import struct
+import zlib
+from pathlib import Path
+
+TOP = (0x1D, 0x27, 0x3C)      # background gradient, top
+BOTTOM = (0x0A, 0x0D, 0x14)   # background gradient, bottom
+GLYPH = (0xEE, 0xF2, 0xF9)    # the wave itself
+
+STATIC = Path(__file__).resolve().parent.parent / "static"
+SAMPLES = 3                   # supersampling per axis, for smooth edges
+
+
+def coverage(x: float, y: float, size: float) -> float:
+    """How much of the glyph covers this point: a dot plus three arcs
+    opening to the right, i.e. the usual 'sound coming out' mark."""
+    cx, cy = 0.33 * size, 0.5 * size
+    dx, dy = x - cx, y - cy
+    distance = math.hypot(dx, dy)
+
+    if distance <= 0.075 * size:
+        return 1.0
+
+    angle = abs(math.degrees(math.atan2(dy, dx)))
+    if angle > 50:
+        return 0.0
+
+    half = 0.024 * size
+    for radius in (0.17, 0.27, 0.37):
+        if abs(distance - radius * size) <= half:
+            return 1.0
+    return 0.0
+
+
+def render(size: int) -> bytes:
+    rows = bytearray()
+    step = 1.0 / SAMPLES
+    for py in range(size):
+        rows.append(0)  # PNG filter type 0 for this scanline
+        mix = py / max(1, size - 1)
+        background = tuple(
+            round(TOP[i] + (BOTTOM[i] - TOP[i]) * mix) for i in range(3)
+        )
+        for px in range(size):
+            hits = 0
+            for sy in range(SAMPLES):
+                for sx in range(SAMPLES):
+                    if coverage(px + (sx + 0.5) * step, py + (sy + 0.5) * step, size):
+                        hits += 1
+            alpha = hits / (SAMPLES * SAMPLES)
+            if alpha == 0:
+                rows.extend(background)
+            else:
+                rows.extend(
+                    round(background[i] + (GLYPH[i] - background[i]) * alpha) for i in range(3)
+                )
+    return bytes(rows)
+
+
+def write_png(path: Path, size: int, raw: bytes):
+    def chunk(kind: bytes, data: bytes) -> bytes:
+        return (struct.pack(">I", len(data)) + kind + data
+                + struct.pack(">I", zlib.crc32(kind + data) & 0xFFFFFFFF))
+
+    header = struct.pack(">IIBBBBB", size, size, 8, 2, 0, 0, 0)  # 8-bit truecolour
+    path.write_bytes(
+        b"\x89PNG\r\n\x1a\n"
+        + chunk(b"IHDR", header)
+        + chunk(b"IDAT", zlib.compress(raw, 9))
+        + chunk(b"IEND", b"")
+    )
+
+
+if __name__ == "__main__":
+    for size in (180, 512):
+        target = STATIC / f"icon-{size}.png"
+        write_png(target, size, render(size))
+        print(f"wrote {target} ({target.stat().st_size} bytes)")