What's the use case for the information supplied by the class method in such cases? What does it really tell me to be of practical use? It doesn't seem to have anything to do with inheritance.
class works the same way for every object. Calling class on a class provides the same information as calling class on an instance. That's because in Ruby, classes are instances, too.
'foo'.class returns String because 'foo' is an instance of String. Likewise, User.class returns Class because User is an instance of Class.
In particular, User is not an instance of ApplicationRecord.
It might not be obvious that User is an instance of Class when creating it via the class keyword:
class User < ApplicationRecord; end
But it becomes very obvious when you create it explicitly via Class.new: (both examples produce the same result)
User = Class.new(ApplicationRecord)
User.class #=> Class
Because the above is just like: (using String.new for demonstration purposes)
foo = String.new('foo')
foo.class #=> String