No, I can use the external css. The issue was with the __ name __ present in the Dash class constructor. It worked now after removing __ name __ from the Dash class constructor. No idea why it created the issue.
But after removing the __ name __, the new issue appeared. The stylesheets in the assets folder aren’t served anymore. So I need to fix that __ name __ issue.
There is a thread discussing why having __ name __ is important. See it at How do I use Dash to add local css?