feat(auth): implement user authentication and email verification

Add registration, login, and logout flows with session management
Integrate Resend for email verification tokens
Create frontend auth views and update topbar state

backend/db/schema.sql

@@ -3,6 +3,41 @@ CREATE TABLE IF NOT EXISTS environments (
   name text NOT NULL UNIQUE
 );
 
+CREATE TABLE IF NOT EXISTS users (
+  id integer GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
+  email text NOT NULL UNIQUE,
+  display_name text NOT NULL,
+  password_hash text NOT NULL,
+  email_verified_at timestamptz,
+  created_at timestamptz NOT NULL DEFAULT now(),
+  updated_at timestamptz NOT NULL DEFAULT now(),
+  CHECK (email = lower(email)),
+  CHECK (length(display_name) BETWEEN 1 AND 40)
+);
+
+CREATE TABLE IF NOT EXISTS email_verification_tokens (
+  id integer GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
+  user_id integer NOT NULL REFERENCES users(id) ON DELETE CASCADE,
+  token_hash text NOT NULL UNIQUE,
+  expires_at timestamptz NOT NULL,
+  used_at timestamptz,
+  created_at timestamptz NOT NULL DEFAULT now()
+);
+
+CREATE INDEX IF NOT EXISTS email_verification_tokens_user_id_idx
+  ON email_verification_tokens(user_id);
+
+CREATE TABLE IF NOT EXISTS user_sessions (
+  id integer GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
+  user_id integer NOT NULL REFERENCES users(id) ON DELETE CASCADE,
+  token_hash text NOT NULL UNIQUE,
+  expires_at timestamptz NOT NULL,
+  created_at timestamptz NOT NULL DEFAULT now()
+);
+
+CREATE INDEX IF NOT EXISTS user_sessions_user_id_idx
+  ON user_sessions(user_id);
+
 CREATE TABLE IF NOT EXISTS skills (
   id integer GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
   name text NOT NULL,