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/lobby.go

@@ -6,20 +6,21 @@ import (
 )
 
 type LobbyProps struct {
-	NicknameBind       h.H
-	CreateGameKeyDown  h.H
-	CreateGameClick    h.H
-	IsLoggedIn         bool
-	Username           string
-	LogoutClick        h.H
-	UserGames          []GameListItem
-	DeleteGameClick    func(id string) h.H
-	ActiveTab          string
-	TabClickConnect4   h.H
-	TabClickSnake      h.H
-	SnakeNicknameBind  h.H
-	SnakePresetClicks  []h.H
-	ActiveSnakeGames   []*snake.SnakeGame
+	NicknameBind        h.H
+	CreateGameKeyDown   h.H
+	CreateGameClick     h.H
+	IsLoggedIn          bool
+	Username            string
+	LogoutClick         h.H
+	UserGames           []GameListItem
+	DeleteGameClick     func(id string) h.H
+	ActiveTab           string
+	TabClickConnect4    h.H
+	TabClickSnake       h.H
+	SnakeNicknameBind   h.H
+	SnakeSoloClicks     []h.H
+	SnakeMultiClicks    []h.H
+	ActiveSnakeGames    []*snake.SnakeGame
 }
 
 func LobbyView(p LobbyProps) h.H {
@@ -40,7 +41,7 @@ func LobbyView(p LobbyProps) h.H {
 
 	var tabContent h.H
 	if p.ActiveTab == "snake" {
-		tabContent = SnakeLobbyTab(p.SnakeNicknameBind, p.SnakePresetClicks, p.ActiveSnakeGames)
+		tabContent = SnakeLobbyTab(p.SnakeNicknameBind, p.SnakeSoloClicks, p.SnakeMultiClicks, p.ActiveSnakeGames)
 	} else {
 		tabContent = connect4LobbyContent(p)
 	}