Try to remove and install again 'IntelliSense for CSS class names in HTML' here is the link, you could follow the guide to use it. ;)
https://marketplace.visualstudio.com/items?itemName=Zignd.html-css-class-completion
https://stackoverflow.com/a/65503147/11382670
According to @Jason Chuot, switching to version 0.2.3 still works. The extension in my question called as "HTML CSS Support". which wasnt working for me at the latest version. Now, I switched to 0.2.3 and it works!