Forwarding subdirectory under a main site to a subdomain

I have a main site that is deployed on Netlify eg : www.example.com

And I have a subdirectory under this main site called blog eg : www.example.com/blog

As per the below community post, I have created another Netlify site [sleepy-roentgen-3eb28f]
eg : blog.example.com with redirect rule in the site’s Ntelify.toml

And I followed the below too
https://answers.netlify.com/t/forwarding-subdomain-to-a-path/2988/3

But when I browse the URL on the browser for the blog content, I see the URL change from www.example.com/blog/post-1 to blog.example.com/blog/post-1 instead of there being no change.

Hey @indcoder,
Is the expected result that https://www.hackmum.in/blog/* would redirect behind the scenes to https://blog.hackmum.in/*?

If that’s the case, could you please post the netlify.toml of your https://www.hackmum.in site? Thank you!