tools: check links in api docs

Fixes: nodejs#35189

PR-URL: nodejs#35191
Reviewed-By: Derek Lewis <DerekNonGeneric@inf.is>
Reviewed-By: Jiawen Geng <technicalcute@gmail.com>
Reviewed-By: Trivikram Kamat <trivikr.dev@gmail.com>
Reviewed-By: Richard Lau <riclau@uk.ibm.com>
Reviewed-By: Rich Trott <rtrott@gmail.com>

tools/doc/checkLinks.js

@@ -26,7 +26,6 @@ function findMarkdownFilesRecursively(dirPath) {
 
     if (
       entry.isDirectory() &&
-      entry.name !== 'api' &&
       entry.name !== 'build' &&
       entry.name !== 'changelogs' &&
       entry.name !== 'deps' &&