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

main.go

@@ -152,17 +152,27 @@ func main() {
 			snakeNickname = c.Signal(username)
 		}
 
-		// Snake create game actions — one per preset
-		var snakePresetClicks []h.H
+		// Snake create game actions — one per preset for solo and multiplayer
+		var snakeSoloClicks []h.H
+		var snakeMultiClicks []h.H
 		for _, preset := range snake.GridPresets {
 			w, ht := preset.Width, preset.Height
-			snakePresetClicks = append(snakePresetClicks, c.Action(func() {
+			snakeSoloClicks = append(snakeSoloClicks, c.Action(func() {
 				name := snakeNickname.String()
 				if name == "" {
 					return
 				}
 				c.Session().Set("nickname", name)
-				si := snakeStore.Create(w, ht)
+				si := snakeStore.Create(w, ht, snake.ModeSinglePlayer)
+				c.Redirectf("/snake/%s", si.ID())
+			}).OnClick())
+			snakeMultiClicks = append(snakeMultiClicks, c.Action(func() {
+				name := snakeNickname.String()
+				if name == "" {
+					return
+				}
+				c.Session().Set("nickname", name)
+				si := snakeStore.Create(w, ht, snake.ModeMultiplayer)
 				c.Redirectf("/snake/%s", si.ID())
 			}).OnClick())
 		}
@@ -181,7 +191,8 @@ func main() {
 				TabClickConnect4:  tabClickConnect4.OnClick(),
 				TabClickSnake:     tabClickSnake.OnClick(),
 				SnakeNicknameBind: snakeNickname.Bind(),
-				SnakePresetClicks: snakePresetClicks,
+				SnakeSoloClicks:   snakeSoloClicks,
+				SnakeMultiClicks:  snakeMultiClicks,
 				ActiveSnakeGames:  snakeStore.ActiveGames(),
 			})
 		})
@@ -599,7 +610,8 @@ func main() {
 				content = append(content, ui.SnakeBoard(sg))
 			}
 
-			if sg.Status == snake.StatusWaitingForPlayers || sg.Status == snake.StatusCountdown {
+			// Only show invite link for multiplayer games
+			if sg.Mode == snake.ModeMultiplayer && (sg.Status == snake.StatusWaitingForPlayers || sg.Status == snake.StatusCountdown) {
 				content = append(content, ui.SnakeInviteLink(sg.ID))
 			}