IntelliJ does not show 'Class' when we right click and select 'New'

you need to mark your directory as source root (right click on the parent directory)

and then compile the plugin (it is important )

as result you will be able to add classes and more

The directory or one of the parent directories must be marked as Source Root (In this case, it appears in blue).

If this is not the case, right click your root source directory -> Mark As -> Source Root.

This can also happen if your package name is invalid.

For example, if your "package" is com.my-company (which is not a valid Java package name due to the dash), IntelliJ will prevent you from creating a Java Class in that package.

If you open your module settings (F4) you can nominate which paths contain 'source'. Intellij will then mark these directories in blue and allow you to add classes etc.

In a similar fashion you can highlight test directories for unit tests.