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

snake/logic.go

@@ -152,8 +152,12 @@ func RemoveFood(state *GameState, indices []int) {
 }
 
 // SpawnFood adds food items to maintain the target count.
-func SpawnFood(state *GameState, playerCount int) {
+// Single player always maintains exactly 1 food for classic snake feel.
+func SpawnFood(state *GameState, playerCount int, mode GameMode) {
 	target := playerCount/2 + 1
+	if mode == ModeSinglePlayer {
+		target = 1
+	}
 	for len(state.Food) < target {
 		p := randomEmptyCell(state)
 		if p == nil {