refactor: move DB to shared crate, convert push endpoints to server functions, remove dead REST handlers

shared/migrations/001_init.sql

@@ -0,0 +1,16 @@
+-- 001_init.sql
+-- Initial schema for users and sessions
+
+CREATE TABLE IF NOT EXISTS users (
+    id INTEGER PRIMARY KEY,
+    username TEXT NOT NULL UNIQUE,
+    password_hash TEXT NOT NULL,
+    created_at DATETIME DEFAULT CURRENT_TIMESTAMP
+);
+
+CREATE TABLE IF NOT EXISTS sessions (
+    token TEXT PRIMARY KEY,
+    user_id INTEGER NOT NULL,
+    expires_at DATETIME NOT NULL,
+    FOREIGN KEY(user_id) REFERENCES users(id)
+);