But we do have a sub-category as well. So, does the cloudflare do same things for the subdirectory automatically, OR do we need to separately add our subdirectory to Cloudflare.
If you mean “subdomain” like sub.example.com, then you would have another DNS record. As long as it is set to Proxied, then it will use Cloudflare.
If you mean a directory on your site, like https://example.com/sub-category, then it is already part of the example.com hostname that’s using Cloudflare.