How to make custom_header_setup() image as background image?

Because you have used it as an image.
<img src="https://..." height="..." width="..."/>

This code is used to display images, not background images.

Use it with text:

<div style="background-image: url(../images/test-background.gif); height: 200px; width: 400px; border: 1px solid black;">Example of a DIV element with a background image:</div>

Or without text:

<div style="background-image: url(../images/test-background.gif); height: 200px; width: 400px; border: 1px solid black;"> </div>

Source is enter link description here

I tried it with the header tag…

<header style="background-image: url(.../images.png)";>
Your text here.
</header>