feat(display): add reuse flag to Display protocol

- Add reuse parameter to Display.init() for all backends
- PygameDisplay: reuse existing SDL window via class-level flag
- TerminalDisplay: skip re-init when reuse=True
- WebSocketDisplay: skip server start when reuse=True
- SixelDisplay, KittyDisplay, NullDisplay: ignore reuse (not applicable)
- MultiDisplay: pass reuse to child displays
- Update benchmark.py to reuse pygame display for effect benchmarks
- Add test_websocket_e2e.py with e2e marker
- Register e2e marker in pyproject.toml

engine/display/backends/kitty.py

@@ -126,7 +126,14 @@ class KittyDisplay:
         self._initialized = False
         self._font_path = None
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: Ignored for KittyDisplay (protocol doesn't support reuse)
+        """
         self.width = width
         self.height = height
         self._initialized = True

engine/display/backends/multi.py

@@ -4,7 +4,10 @@ Multi display backend - forwards to multiple displays.
 
 
 class MultiDisplay:
-    """Display that forwards to multiple displays."""
+    """Display that forwards to multiple displays.
+
+    Supports reuse - passes reuse flag to all child displays.
+    """
 
     width: int = 80
     height: int = 24
@@ -14,11 +17,18 @@ class MultiDisplay:
         self.width = 80
         self.height = 24
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize all child displays with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: If True, use reuse mode for child displays
+        """
         self.width = width
         self.height = height
         for d in self.displays:
-            d.init(width, height)
+            d.init(width, height, reuse=reuse)
 
     def show(self, buffer: list[str]) -> None:
         for d in self.displays:

engine/display/backends/null.py

@@ -6,12 +6,23 @@ import time
 
 
 class NullDisplay:
-    """Headless/null display - discards all output."""
+    """Headless/null display - discards all output.
+
+    This display does nothing - useful for headless benchmarking
+    or when no display output is needed.
+    """
 
     width: int = 80
     height: int = 24
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: Ignored for NullDisplay (no resources to reuse)
+        """
         self.width = width
         self.height = height
 

engine/display/backends/pygame.py

@@ -6,12 +6,16 @@ import time
 
 
 class PygameDisplay:
-    """Pygame display backend - renders to native window."""
+    """Pygame display backend - renders to native window.
+
+    Supports reuse mode - when reuse=True, skips SDL initialization
+    and reuses the existing pygame window from a previous instance.
+    """
 
     width: int = 80
-    height: int = 24
     window_width: int = 800
     window_height: int = 600
+    _pygame_initialized: bool = False
 
     def __init__(
         self,
@@ -76,20 +80,37 @@ class PygameDisplay:
 
         return None
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: If True, attach to existing pygame window instead of creating new
+        """
         self.width = width
         self.height = height
 
+        import os
+
+        os.environ["SDL_VIDEODRIVER"] = "x11"
+
         try:
             import pygame
         except ImportError:
             return
 
+        if reuse and PygameDisplay._pygame_initialized:
+            self._pygame = pygame
+            self._initialized = True
+            return
+
         pygame.init()
-        self._pygame = pygame
+        pygame.display.set_caption("Mainline")
 
         self._screen = pygame.display.set_mode((self.window_width, self.window_height))
-        pygame.display.set_caption("Mainline")
+        self._pygame = pygame
+        PygameDisplay._pygame_initialized = True
 
         font_path = self._get_font_path()
         if font_path:
@@ -218,6 +239,18 @@ class PygameDisplay:
             self._screen.fill((0, 0, 0))
             self._pygame.display.flip()
 
-    def cleanup(self) -> None:
-        if self._pygame:
+    def cleanup(self, quit_pygame: bool = True) -> None:
+        """Cleanup display resources.
+
+        Args:
+            quit_pygame: If True, quit pygame entirely. Set to False when
+                        reusing the display to avoid closing shared window.
+        """
+        if quit_pygame and self._pygame:
             self._pygame.quit()
+            PygameDisplay._pygame_initialized = False
+
+    @classmethod
+    def reset_state(cls) -> None:
+        """Reset pygame state - useful for testing."""
+        cls._pygame_initialized = False

engine/display/backends/sixel.py

@@ -271,7 +271,14 @@ class SixelDisplay:
 
         return None
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: Ignored for SixelDisplay
+        """
         self.width = width
         self.height = height
         self._initialized = True

engine/display/backends/terminal.py

@@ -6,17 +6,32 @@ import time
 
 
 class TerminalDisplay:
-    """ANSI terminal display backend."""
+    """ANSI terminal display backend.
+
+    Renders buffer to stdout using ANSI escape codes.
+    Supports reuse - when reuse=True, skips re-initializing terminal state.
+    """
 
     width: int = 80
     height: int = 24
+    _initialized: bool = False
 
-    def init(self, width: int, height: int) -> None:
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: If True, skip terminal re-initialization
+        """
         from engine.terminal import CURSOR_OFF
 
         self.width = width
         self.height = height
-        print(CURSOR_OFF, end="", flush=True)
+
+        if not reuse or not self._initialized:
+            print(CURSOR_OFF, end="", flush=True)
+            self._initialized = True
 
     def show(self, buffer: list[str]) -> None:
         import sys

engine/display/backends/websocket.py

@@ -86,12 +86,20 @@ class WebSocketDisplay:
         """Check if WebSocket support is available."""
         return self._available
 
-    def init(self, width: int, height: int) -> None:
-        """Initialize display with dimensions and start server."""
+    def init(self, width: int, height: int, reuse: bool = False) -> None:
+        """Initialize display with dimensions and start server.
+
+        Args:
+            width: Terminal width in characters
+            height: Terminal height in rows
+            reuse: If True, skip starting servers (assume already running)
+        """
         self.width = width
         self.height = height
-        self.start_server()
-        self.start_http_server()
+
+        if not reuse or not self._server_running:
+            self.start_server()
+            self.start_http_server()
 
     def show(self, buffer: list[str]) -> None:
         """Broadcast buffer to all connected clients."""