functions.php inject inline css

The easiest way I’ve seen is to echo it where you need it:

function inline_css() {
  echo "<style>html{background-color:#001337}</style>";
}
add_action( 'wp_head', 'inline_css', 0 );

Since 2019 you can also add styles inline inside the body, shown here without using echo:

function example_body_open () { ?>
  <style>
    html {
      background-color: #B4D455;
    }
  </style>
<?php }
add_action( 'wp_body_open', 'example_body_open' );

The benefit here is you get better syntax highlighting and do not need to escape double-quotes. Note this particular hook will only work with themes implementing wp_body_open hook.