This seems to be obvious, but you can expect Rake tasks to be called in RSpec.

it 'deletes all Users' do
   FactroyBot.create(:user)
   expect(Rake::Task['notify:critical_operation']).to receive(:invoke)
   
   expect { described_class.clean }.to change(User, :count).from(1).to(0) 
end

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Note: Try to avoid logic in rake tasks and prefer to just call classes in them.

Example:

desc 'Some task'
task :some_task do
  SomeClass.new.run
end