Optimize numpy pipeline, add per-stage timing, and auto-sync LED count

- Eliminate 5 numpy↔tuple conversions per frame in processing hot path:
  map_border_to_leds returns ndarray, inline numpy smoothing with integer
  math, send_pixels_fast accepts ndarray directly
- Fix numpy boolean bug in keepalive check (use `is not None`)
- Add per-stage pipeline timing (extract/map/smooth/send) to metrics API
  and UI with color-coded breakdown bar
- Expose device_fps from WLED health check in API schemas
- Auto-sync LED count from WLED device: health check detects changes and
  updates storage, calibration, and active targets automatically
- Use integer math for brightness scaling (uint16 * brightness >> 8)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/wled_controller/api/schemas/devices.py

@@ -115,6 +115,7 @@ class DeviceStateResponse(BaseModel):
     device_led_count: Optional[int] = Field(None, description="LED count reported by device")
     device_rgbw: Optional[bool] = Field(None, description="Whether device uses RGBW LEDs")
     device_led_type: Optional[str] = Field(None, description="LED chip type (e.g. WS2812B, SK6812 RGBW)")
+    device_fps: Optional[int] = Field(None, description="Device-reported FPS (WLED internal refresh rate)")
     device_last_checked: Optional[datetime] = Field(None, description="Last health check time")
     device_error: Optional[str] = Field(None, description="Last health check error")
     test_mode: bool = Field(default=False, description="Whether calibration test mode is active")

server/src/wled_controller/api/schemas/picture_targets.py

@@ -128,6 +128,11 @@ class TargetProcessingState(BaseModel):
     frames_skipped: Optional[int] = Field(None, description="Frames skipped (no screen change)")
     frames_keepalive: Optional[int] = Field(None, description="Keepalive frames sent during standby")
     fps_current: Optional[int] = Field(None, description="Frames sent in the last second")
+    timing_extract_ms: Optional[float] = Field(None, description="Border extraction time (ms)")
+    timing_map_leds_ms: Optional[float] = Field(None, description="LED mapping time (ms)")
+    timing_smooth_ms: Optional[float] = Field(None, description="Smoothing time (ms)")
+    timing_send_ms: Optional[float] = Field(None, description="DDP send time (ms)")
+    timing_total_ms: Optional[float] = Field(None, description="Total processing time (ms)")
     display_index: int = Field(default=0, description="Current display index")
     last_update: Optional[datetime] = Field(None, description="Last successful update")
     errors: List[str] = Field(default_factory=list, description="Recent errors")
@@ -138,6 +143,7 @@ class TargetProcessingState(BaseModel):
     device_led_count: Optional[int] = Field(None, description="LED count reported by device")
     device_rgbw: Optional[bool] = Field(None, description="Whether device uses RGBW LEDs")
     device_led_type: Optional[str] = Field(None, description="LED chip type (e.g. WS2812B, SK6812 RGBW)")
+    device_fps: Optional[int] = Field(None, description="Device-reported FPS (WLED internal refresh rate)")
     device_last_checked: Optional[datetime] = Field(None, description="Last health check time")
     device_error: Optional[str] = Field(None, description="Last health check error")