fix(completions): resolve Windows compatibility issues in zsh-installer tests

- Fix canWriteFile to use fs.access with W_OK flag instead of Unix-style
  permission bits (stats.mode & 0o222) which don't work on Windows
- Update test paths to use platform-specific invalid paths that fail on
  both Unix and Windows
- Use regex for path separator matching in test assertions

src/utils/file-system.ts

@@ -1,4 +1,4 @@
-import { promises as fs } from 'fs';
+import { promises as fs, constants as fsConstants } from 'fs';
 import path from 'path';
 
 function isMarkerOnOwnLine(content: string, markerIndex: number, markerLength: number): boolean {
@@ -93,10 +93,24 @@ export class FileSystemUtils {
         return true;
       }
 
-      return (stats.mode & 0o222) !== 0;
+      // On Windows, stats.mode doesn't reliably indicate write permissions.
+      // Use fs.access with W_OK to check actual write permissions cross-platform.
+      try {
+        await fs.access(filePath, fsConstants.W_OK);
+        return true;
+      } catch {
+        return false;
+      }
     } catch (error: any) {
       if (error.code === 'ENOENT') {
-        return true;
+        // File doesn't exist; check if we can write to the parent directory
+        const parentDir = path.dirname(filePath);
+        try {
+          await fs.access(parentDir, fsConstants.W_OK);
+          return true;
+        } catch {
+          return false;
+        }
       }
 
       console.debug(`Unable to determine write permissions for ${filePath}: ${error.message}`);

test/core/completions/installers/zsh-installer.test.ts

@@ -195,7 +195,11 @@ describe('ZshInstaller', () => {
 
     it('should handle installation errors gracefully', async () => {
       // Create installer with non-existent/invalid home directory
-      const invalidInstaller = new ZshInstaller('/root/invalid/nonexistent/path');
+      // Use a path that will fail on both Unix and Windows
+      const invalidPath = process.platform === 'win32'
+        ? 'Z:\\nonexistent\\invalid\\path'  // Non-existent drive letter on Windows
+        : '/root/invalid/nonexistent/path';  // Permission-denied path on Unix
+      const invalidInstaller = new ZshInstaller(invalidPath);
 
       const result = await invalidInstaller.install(testScript);
 
@@ -503,7 +507,11 @@ describe('ZshInstaller', () => {
 
     it('should handle write permission errors gracefully', async () => {
       // Create installer with path that can't be written
-      const invalidInstaller = new ZshInstaller('/root/invalid/path');
+      // Use a path that will fail on both Unix and Windows
+      const invalidPath = process.platform === 'win32'
+        ? 'Z:\\nonexistent\\invalid\\path'  // Non-existent drive letter on Windows
+        : '/root/invalid/path';  // Permission-denied path on Unix
+      const invalidInstaller = new ZshInstaller(invalidPath);
 
       const result = await invalidInstaller.configureZshrc(completionsDir);
 
@@ -641,7 +649,8 @@ describe('ZshInstaller', () => {
       if (exists) {
         const content = await fs.readFile(zshrcPath, 'utf-8');
         expect(content).toContain('fpath=');
-        expect(content).toContain('custom/completions');
+        // Check for custom/completions or custom\completions (Windows path separator)
+        expect(content).toMatch(/custom[/\\]completions/);
       }
     });