feat(hooks): add shared resolve-formatter utility with caching

Extract project-root discovery, formatter detection, and binary
resolution into a reusable module. Caches results per-process to
avoid redundant filesystem lookups on every Edit hook invocation.

This is the foundation for eliminating npx overhead in format hooks.

scripts/lib/resolve-formatter.js

@@ -0,0 +1,156 @@
+/**
+ * Shared formatter resolution utilities with caching.
+ *
+ * Extracts project-root discovery, formatter detection, and binary
+ * resolution into a single module so that post-edit-format.js and
+ * quality-gate.js avoid duplicating work and filesystem lookups.
+ */
+
+'use strict';
+
+const fs = require('fs');
+const path = require('path');
+
+// ── Caches (per-process, cleared on next hook invocation) ───────────
+const projectRootCache = new Map();
+const formatterCache = new Map();
+const binCache = new Map();
+
+// ── Public helpers ──────────────────────────────────────────────────
+
+/**
+ * Walk up from `startDir` until a directory containing package.json is found.
+ * Returns `startDir` as fallback when no package.json exists above it.
+ *
+ * @param {string} startDir - Absolute directory path to start from
+ * @returns {string} Absolute path to the project root
+ */
+function findProjectRoot(startDir) {
+  if (projectRootCache.has(startDir)) return projectRootCache.get(startDir);
+
+  let dir = startDir;
+  while (dir !== path.dirname(dir)) {
+    if (fs.existsSync(path.join(dir, 'package.json'))) {
+      projectRootCache.set(startDir, dir);
+      return dir;
+    }
+    dir = path.dirname(dir);
+  }
+
+  projectRootCache.set(startDir, startDir);
+  return startDir;
+}
+
+/**
+ * Detect the formatter configured in the project.
+ * Biome takes priority over Prettier.
+ *
+ * @param {string} projectRoot - Absolute path to the project root
+ * @returns {'biome' | 'prettier' | null}
+ */
+function detectFormatter(projectRoot) {
+  if (formatterCache.has(projectRoot)) return formatterCache.get(projectRoot);
+
+  const biomeConfigs = ['biome.json', 'biome.jsonc'];
+  for (const cfg of biomeConfigs) {
+    if (fs.existsSync(path.join(projectRoot, cfg))) {
+      formatterCache.set(projectRoot, 'biome');
+      return 'biome';
+    }
+  }
+
+  const prettierConfigs = [
+    '.prettierrc',
+    '.prettierrc.json',
+    '.prettierrc.js',
+    '.prettierrc.cjs',
+    '.prettierrc.mjs',
+    '.prettierrc.yml',
+    '.prettierrc.yaml',
+    '.prettierrc.toml',
+    'prettier.config.js',
+    'prettier.config.cjs',
+    'prettier.config.mjs',
+  ];
+  for (const cfg of prettierConfigs) {
+    if (fs.existsSync(path.join(projectRoot, cfg))) {
+      formatterCache.set(projectRoot, 'prettier');
+      return 'prettier';
+    }
+  }
+
+  formatterCache.set(projectRoot, null);
+  return null;
+}
+
+/**
+ * Resolve the formatter binary, preferring the local node_modules/.bin
+ * installation over npx to avoid package-resolution overhead.
+ *
+ * @param {string} projectRoot - Absolute path to the project root
+ * @param {'biome' | 'prettier'} formatter - Detected formatter name
+ * @returns {{ bin: string, prefix: string[] }}
+ *   `bin`    – executable path (absolute local path or npx/npx.cmd)
+ *   `prefix` – extra args to prepend (e.g. ['@biomejs/biome'] when using npx)
+ */
+function resolveFormatterBin(projectRoot, formatter) {
+  const cacheKey = `${projectRoot}:${formatter}`;
+  if (binCache.has(cacheKey)) return binCache.get(cacheKey);
+
+  const isWin = process.platform === 'win32';
+  const npxBin = isWin ? 'npx.cmd' : 'npx';
+
+  if (formatter === 'biome') {
+    const localBin = path.join(
+      projectRoot,
+      'node_modules',
+      '.bin',
+      isWin ? 'biome.cmd' : 'biome',
+    );
+    if (fs.existsSync(localBin)) {
+      const result = { bin: localBin, prefix: [] };
+      binCache.set(cacheKey, result);
+      return result;
+    }
+    const result = { bin: npxBin, prefix: ['@biomejs/biome'] };
+    binCache.set(cacheKey, result);
+    return result;
+  }
+
+  if (formatter === 'prettier') {
+    const localBin = path.join(
+      projectRoot,
+      'node_modules',
+      '.bin',
+      isWin ? 'prettier.cmd' : 'prettier',
+    );
+    if (fs.existsSync(localBin)) {
+      const result = { bin: localBin, prefix: [] };
+      binCache.set(cacheKey, result);
+      return result;
+    }
+    const result = { bin: npxBin, prefix: ['prettier'] };
+    binCache.set(cacheKey, result);
+    return result;
+  }
+
+  const result = { bin: npxBin, prefix: [] };
+  binCache.set(cacheKey, result);
+  return result;
+}
+
+/**
+ * Clear all caches. Useful for testing.
+ */
+function clearCaches() {
+  projectRootCache.clear();
+  formatterCache.clear();
+  binCache.clear();
+}
+
+module.exports = {
+  findProjectRoot,
+  detectFormatter,
+  resolveFormatterBin,
+  clearCaches,
+};