How to display user’s avatar on the top of main menu in WordPress admin panel?

I’m not sure if core offers any hooks well suited to this purpose. I certainly don’t see any purpose-fit hooks in the source which renders the admin menu.

But on a more hacky whim, this could be relatively easily accomplished using a add_menu_item() with $position 0, then modifying the new menu item registration in the $menu global in order to adjust any parameters as necessary.

function wpse391894_admin_menu_avatar() {
  global $menu;

  $user  = wp_get_current_user();
  $title = sprintf(
    __( 'Howdy, %s', 'wpse391894' ),
    esc_html( $user->display_name )
  );
  $img   = get_avatar( $user );

  add_menu_page(
    $title,
    sprintf(
      "%s\n%s",
      $img,
      $title
    ),
    'read',
    'wpse391894-dummy-slug',
    '',
    'none',
    0
  );

  // Look up a reference to the new menu item registration array.
  $item = &$menu[ array_key_last( $menu ) ];

  // Modify the link?
  $item[2] = "user-edit.php?user_id={$user->ID}";
}

add_action( 'admin_menu', 'wpse391894_admin_menu_avatar' );