feat: add Google Sign-In with JWT auth and Neon DB persistence

internal/db/migrations/002_auth.sql

@@ -0,0 +1,10 @@
+-- Auth: users table
+
+CREATE TABLE IF NOT EXISTS users (
+    id UUID PRIMARY KEY DEFAULT gen_random_uuid(),
+    email TEXT UNIQUE NOT NULL,
+    display_name TEXT NOT NULL,
+    provider TEXT NOT NULL DEFAULT 'google',
+    provider_subject TEXT NOT NULL,
+    created_at TIMESTAMPTZ NOT NULL DEFAULT NOW()
+);