feat(mcp): add package-backed ast-grep MCP

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

packages/ast-grep-mcp/src/cli-binary-path-resolution.ts

@@ -0,0 +1,52 @@
+import { existsSync } from "fs"
+
+import { findSgCliPathSync, getSgCliPath, setSgCliPath } from "./constants"
+
+let resolvedCliPath: string | null = null
+let initPromise: Promise<string | null> | null = null
+
+export async function getAstGrepPath(): Promise<string | null> {
+	if (resolvedCliPath !== null && existsSync(resolvedCliPath)) {
+		return resolvedCliPath
+	}
+
+	if (initPromise) {
+		return initPromise
+	}
+
+	initPromise = (async () => {
+		const syncPath = findSgCliPathSync()
+		if (syncPath && existsSync(syncPath)) {
+			resolvedCliPath = syncPath
+			setSgCliPath(syncPath)
+			return syncPath
+		}
+
+		return null
+	})()
+
+	return initPromise
+}
+
+export function startBackgroundInit(): void {
+	if (!initPromise) {
+		initPromise = getAstGrepPath()
+		initPromise.catch(() => {})
+	}
+}
+
+export function isCliAvailable(): boolean {
+	const path = findSgCliPathSync()
+	return path !== null && existsSync(path)
+}
+
+export async function ensureCliAvailable(): Promise<boolean> {
+	const path = await getAstGrepPath()
+	return path !== null && existsSync(path)
+}
+
+export function getResolvedSgCliPath(): string | null {
+	const path = getSgCliPath()
+	if (path && existsSync(path)) return path
+	return null
+}