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

db/gen/models.go

@@ -22,6 +22,8 @@ type Game struct {
 	GridWidth     sql.NullInt64
 	GridHeight    sql.NullInt64
 	MaxPlayers    int64
+	GameMode      int64
+	Score         int64
 }
 
 type GamePlayer struct {