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/migrations/004_add_snake_mode.sql

@@ -0,0 +1,7 @@
+-- +goose Up
+ALTER TABLE games ADD COLUMN game_mode INTEGER NOT NULL DEFAULT 0;
+ALTER TABLE games ADD COLUMN score INTEGER NOT NULL DEFAULT 0;
+
+-- +goose Down
+ALTER TABLE games DROP COLUMN score;
+ALTER TABLE games DROP COLUMN game_mode;