refactor: modularize display backends and add benchmark runner

- Create engine/display/ package with registry pattern
- Move displays to engine/display/backends/ (terminal, null, websocket, sixel)
- Add DisplayRegistry with auto-discovery
- Add benchmark.py for performance testing effects × displays matrix
- Add mise tasks: benchmark, benchmark-json, benchmark-report
- Update controller to use new display module

engine/display/__init__.py

@@ -0,0 +1,102 @@
+"""
+Display backend system with registry pattern.
+
+Allows swapping output backends via the Display protocol.
+Supports auto-discovery of display backends.
+"""
+
+from typing import Protocol
+
+from engine.display.backends.multi import MultiDisplay
+from engine.display.backends.null import NullDisplay
+from engine.display.backends.sixel import SixelDisplay
+from engine.display.backends.terminal import TerminalDisplay
+from engine.display.backends.websocket import WebSocketDisplay
+
+
+class Display(Protocol):
+    """Protocol for display backends."""
+
+    width: int
+    height: int
+
+    def init(self, width: int, height: int) -> None:
+        """Initialize display with dimensions."""
+        ...
+
+    def show(self, buffer: list[str]) -> None:
+        """Show buffer on display."""
+        ...
+
+    def clear(self) -> None:
+        """Clear display."""
+        ...
+
+    def cleanup(self) -> None:
+        """Shutdown display."""
+        ...
+
+
+class DisplayRegistry:
+    """Registry for display backends with auto-discovery."""
+
+    _backends: dict[str, type[Display]] = {}
+    _initialized = False
+
+    @classmethod
+    def register(cls, name: str, backend_class: type[Display]) -> None:
+        """Register a display backend."""
+        cls._backends[name.lower()] = backend_class
+
+    @classmethod
+    def get(cls, name: str) -> type[Display] | None:
+        """Get a display backend class by name."""
+        return cls._backends.get(name.lower())
+
+    @classmethod
+    def list_backends(cls) -> list[str]:
+        """List all available display backend names."""
+        return list(cls._backends.keys())
+
+    @classmethod
+    def create(cls, name: str, **kwargs) -> Display | None:
+        """Create a display instance by name."""
+        backend_class = cls.get(name)
+        if backend_class:
+            return backend_class(**kwargs)
+        return None
+
+    @classmethod
+    def initialize(cls) -> None:
+        """Initialize and register all built-in backends."""
+        if cls._initialized:
+            return
+
+        cls.register("terminal", TerminalDisplay)
+        cls.register("null", NullDisplay)
+        cls.register("websocket", WebSocketDisplay)
+        cls.register("sixel", SixelDisplay)
+
+        cls._initialized = True
+
+
+def get_monitor():
+    """Get the performance monitor."""
+    try:
+        from engine.effects.performance import get_monitor as _get_monitor
+
+        return _get_monitor()
+    except Exception:
+        return None
+
+
+__all__ = [
+    "Display",
+    "DisplayRegistry",
+    "get_monitor",
+    "TerminalDisplay",
+    "NullDisplay",
+    "WebSocketDisplay",
+    "SixelDisplay",
+    "MultiDisplay",
+]