How to make an ActionBar button with a NavigationDrawer like in the Habr, VK, etc. application?

Question

Android

I'm making an application in Android Studio, I created an activity with NavigationDrawer according to the proposed template, and I can't customize the home button in the ActionBar.
It looks like this now:

What I don't like:

• The application icon was determined only programmatically (

  getSupportActionBar().setIcon(R.mipmap.ic_launcher);

  ), the application did not react to the :logo entries in the manifest and styles
  
• Only the part where the hamburger is currently hanging is pressed. Moreover, the hamburger itself is too far from the left edge of the screen.
  

I have scoured the internet and have not found an answer to my question.
So how do you make it all look human, like in these applications?

Answer 1

https://developer.android.com/training/implementin...
habrahabr.ru/post/236567

Answer 2

This kind of side menu icon is deprecated. Moreover, it is not recommended to use the application icon in the bar. Recently struggled with a hamburger. As a result, I settled on the standard version - which is offered at the first launch of a new project.
But the look of your menu icon is somewhat... odd. What are your target versions of android in the gradle file?