fix(rules-injector): memoize project-root lookup per process lifecycle

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

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

src/hooks/rules-injector/project-root-finder.ts

@@ -2,6 +2,12 @@ import { existsSync, statSync } from "node:fs";
 import { dirname, join } from "node:path";
 import { PROJECT_MARKERS } from "./constants";
 
+const projectRootCache = new Map<string, string | null>();
+
+export function clearProjectRootCache(): void {
+  projectRootCache.clear();
+}
+
 /**
  * Find project root by walking up from startPath.
  * Checks for PROJECT_MARKERS (.git, pyproject.toml, package.json, etc.)
@@ -10,6 +16,16 @@ import { PROJECT_MARKERS } from "./constants";
  * @returns Project root path or null if not found
  */
 export function findProjectRoot(startPath: string): string | null {
+  if (projectRootCache.has(startPath)) {
+    return projectRootCache.get(startPath) ?? null;
+  }
+
+  const projectRoot = findProjectRootWithoutCache(startPath);
+  projectRootCache.set(startPath, projectRoot);
+  return projectRoot;
+}
+
+function findProjectRootWithoutCache(startPath: string): string | null {
   let current: string;
 
   try {