normalize project structure: src/client + src/server + src/shared

- restructure from src/ + server/ to src/client/ + src/server/ + src/shared/
- switch backend runtime from Node (tsx) to Bun
- merge server/package.json into root, remove @hono/node-server + tsx
- convert server @/ imports to relative paths
- standardize biome config (lineWidth 80, quoteStyle double)
- add CLAUDE.md, .env.example at root
- update vite.config, tsconfig, deploy.sh for new structure

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/client/shared/db/push-state-db.ts

@@ -0,0 +1,28 @@
+import type { PGlite } from "@electric-sql/pglite"
+
+export async function getPushState(
+	db: PGlite,
+	key: string,
+): Promise<string | null> {
+	const res = await db.query<{ value: string }>(
+		"SELECT value FROM push_state WHERE key = $1",
+		[key],
+	)
+	return res.rows.length > 0 ? res.rows[0].value : null
+}
+
+export async function setPushState(
+	db: PGlite,
+	key: string,
+	value: string,
+): Promise<void> {
+	await db.query(
+		`INSERT INTO push_state (key, value) VALUES ($1, $2)
+		 ON CONFLICT (key) DO UPDATE SET value = $2`,
+		[key, value],
+	)
+}
+
+export async function removePushState(db: PGlite, key: string): Promise<void> {
+	await db.query("DELETE FROM push_state WHERE key = $1", [key])
+}