Add adaptive FPS and honest device reachability during streaming

DDP uses fire-and-forget UDP, so when a WiFi device becomes overwhelmed
by sustained traffic, sends appear successful while the device is
actually unreachable. This adds:

- HTTP liveness probe (GET /json/info, 2s timeout) every 10s during
  streaming, exposed as device_streaming_reachable in target state
- Adaptive FPS (opt-in): exponential backoff when device is unreachable,
  gradual recovery when it stabilizes — finds sustainable send rate
- Honest health checks: removed the lie that forced device_online=true
  during streaming; now runs actual health checks regardless
- Target editor toggle, FPS display shows effective rate when throttled,
  health dot reflects streaming reachability, red highlight when
  unreachable
- Auto-backup scheduling support in settings modal

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

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

@@ -79,3 +79,38 @@ class RestoreResponse(BaseModel):
     missing_stores: List[str] = Field(default_factory=list, description="Store keys not found in backup")
     restart_scheduled: bool = Field(description="Whether server restart was scheduled")
     message: str = Field(description="Human-readable status message")
+
+
+# ─── Auto-backup schemas ──────────────────────────────────────
+
+class AutoBackupSettings(BaseModel):
+    """Settings for automatic backup."""
+
+    enabled: bool = Field(description="Whether auto-backup is enabled")
+    interval_hours: float = Field(ge=0.5, le=168, description="Backup interval in hours")
+    max_backups: int = Field(ge=1, le=100, description="Maximum number of backup files to keep")
+
+
+class AutoBackupStatusResponse(BaseModel):
+    """Auto-backup settings plus runtime status."""
+
+    enabled: bool
+    interval_hours: float
+    max_backups: int
+    last_backup_time: str | None = None
+    next_backup_time: str | None = None
+
+
+class BackupFileInfo(BaseModel):
+    """Information about a saved backup file."""
+
+    filename: str
+    size_bytes: int
+    created_at: str
+
+
+class BackupListResponse(BaseModel):
+    """List of saved backup files."""
+
+    backups: List[BackupFileInfo]
+    count: int