feat: add single player snake mode

Add solo mode where players survive as long as possible while tracking
score (food eaten). Single player games start with a shorter 3-second
countdown vs 10 seconds for multiplayer, maintain exactly 1 food item
for classic snake feel, and end when the player dies rather than when
one player remains.

- Add GameMode type (ModeMultiplayer/ModeSinglePlayer) and Score field
- Filter single player games from "Join a Game" lobby list
- Show "Ready?" and "Score: X" UI for single player mode
- Hide invite link for single player games
- Preserve game mode on rematch

ui/snakestatus.go

@@ -12,6 +12,11 @@ import (
 func SnakeStatusBanner(sg *snake.SnakeGame, mySlot int, rematchClick h.H) h.H {
 	switch sg.Status {
 	case snake.StatusWaitingForPlayers:
+		if sg.Mode == snake.ModeSinglePlayer {
+			return h.Div(h.Class("alert bg-base-200 text-xl font-bold"),
+				h.Text("Ready?"),
+			)
+		}
 		return h.Div(h.Class("alert bg-base-200 text-xl font-bold"),
 			h.Text("Waiting for players..."),
 		)
@@ -35,6 +40,12 @@ func SnakeStatusBanner(sg *snake.SnakeGame, mySlot int, rematchClick h.H) h.H {
 				)
 			}
 		}
+		// Show score during single player gameplay
+		if sg.Mode == snake.ModeSinglePlayer {
+			return h.Div(h.Class("alert alert-success text-xl font-bold"),
+				h.Text(fmt.Sprintf("Score: %d", sg.Score)),
+			)
+		}
 		return h.Div(h.Class("alert alert-success text-xl font-bold"),
 			h.Text("Go!"),
 		)
@@ -42,7 +53,11 @@ func SnakeStatusBanner(sg *snake.SnakeGame, mySlot int, rematchClick h.H) h.H {
 	case snake.StatusFinished:
 		var msg string
 		var class string
-		if sg.Winner != nil {
+
+		if sg.Mode == snake.ModeSinglePlayer {
+			msg = fmt.Sprintf("Game Over! Score: %d", sg.Score)
+			class = "alert alert-info text-xl font-bold"
+		} else if sg.Winner != nil {
 			if sg.Winner.Slot == mySlot {
 				msg = "You win!"
 				class = "alert alert-success text-xl font-bold"