ActiveSupport::Concern official documentation question

Question

So I was going over the official documentation about Rails Concerns here and was trying to wrap my head around why their example of plain module mixin doesn't work, and how do Concerns solve this problem.

Why does the code below throw a NoMethodError?

Of course, I tried several approaches in the code on my end to try and comprehend the context, but I just cannot understand why the NoMethodError is being thrown within the self.extended hook in Bar.

module Foo
  def extended(base)
    base.class_eval do
      def self.method_injected_by_foo
        puts "Foo module"
      end
    end
  end
end

module Bar
  extend Foo
  def self.extended(base)
    puts "=== Acestors ==="
    puts base.ancestors # [Host, Bar, Foo, ... , Object, ...]
    puts "===== self ====="
    puts self                                           # Bar
    puts self.methods.include?(:method_injected_by_foo) # true
    puts "===== base ====="
    puts base                                           # Host
    puts base.methods.include?(:method_injected_by_foo) # false
    puts "================"
    base.method_injected_by_foo # NoMethodError
  end
end

class Host
  include Bar
end

To my understanding, although the method_injected_by_foo doesn't exist within the Host class per se, it should be available in the next immediate ancestor (Bar) when looking up the ancestors chain, and call that method.