Add user authentication and game persistence with SQLite

- User registration/login with bcrypt password hashing
- SQLite database with goose migrations and sqlc-generated queries
- Games and players persisted to database, resumable after restart
- Guest play still supported alongside authenticated users
- Auth UI components (login/register forms, auth header, guest banner)

db/migrations/001_initial_schema.sql

@@ -0,0 +1,40 @@
+-- +goose Up
+CREATE TABLE users (
+    id TEXT PRIMARY KEY,
+    username TEXT UNIQUE NOT NULL,
+    password_hash TEXT NOT NULL,
+    created_at DATETIME DEFAULT CURRENT_TIMESTAMP
+);
+CREATE INDEX idx_users_username ON users(username);
+
+CREATE TABLE games (
+    id TEXT PRIMARY KEY,
+    board TEXT NOT NULL,
+    current_turn INTEGER NOT NULL DEFAULT 1,
+    status INTEGER NOT NULL DEFAULT 0,
+    winner_user_id TEXT,
+    winning_cells TEXT,
+    created_at DATETIME DEFAULT CURRENT_TIMESTAMP,
+    updated_at DATETIME DEFAULT CURRENT_TIMESTAMP
+);
+
+CREATE TABLE game_players (
+    game_id TEXT NOT NULL,
+    user_id TEXT,
+    guest_player_id TEXT,
+    nickname TEXT NOT NULL,
+    color INTEGER NOT NULL,
+    slot INTEGER NOT NULL,
+    created_at DATETIME DEFAULT CURRENT_TIMESTAMP,
+    PRIMARY KEY (game_id, slot),
+    FOREIGN KEY (game_id) REFERENCES games(id) ON DELETE CASCADE,
+    FOREIGN KEY (user_id) REFERENCES users(id),
+    CHECK (user_id IS NOT NULL OR guest_player_id IS NOT NULL)
+);
+CREATE INDEX idx_game_players_user ON game_players(user_id);
+CREATE INDEX idx_game_players_guest ON game_players(guest_player_id);
+
+-- +goose Down
+DROP TABLE IF EXISTS game_players;
+DROP TABLE IF EXISTS games;
+DROP TABLE IF EXISTS users;