feat: add SQLite database and persistent task schema

db/schema.sql

@@ -0,0 +1,17 @@
+CREATE TABLE IF NOT EXISTS tasks (
+  id INTEGER PRIMARY KEY AUTOINCREMENT,
+  title TEXT NOT NULL CHECK (length(trim(title)) > 0),
+  description TEXT NOT NULL DEFAULT '',
+  due_date TEXT NOT NULL CHECK (due_date GLOB '[0-9][0-9][0-9][0-9]-[0-9][0-9]-[0-9][0-9]'),
+  topic TEXT NOT NULL CHECK (length(trim(topic)) > 0),
+  status TEXT NOT NULL DEFAULT 'Todo' CHECK (status IN ('Todo', 'In-Progress', 'Complete')),
+  archived_at TEXT,
+  created_at TEXT NOT NULL DEFAULT CURRENT_TIMESTAMP,
+  updated_at TEXT NOT NULL DEFAULT CURRENT_TIMESTAMP
+);
+
+CREATE INDEX IF NOT EXISTS idx_tasks_active_status
+ON tasks (archived_at, status, due_date);
+
+CREATE INDEX IF NOT EXISTS idx_tasks_topic
+ON tasks (topic COLLATE NOCASE);