Add extra body class only to first page of archive, tag, cat

You could use the is_paged() function to conditionally add a body class

https://codex.www.ads-software.com/Function_Reference/is_paged

if you need individual body_classes for each of those webpages, possibly follow this structure:

https://developer.www.ads-software.com/reference/functions/body_class/#comment-1846

and add your conditionals, like is_tag() && !is_paged() and is_category() && !is_paged() and is_page_template('template_file_name.php') && !is_paged()

Thank you (@alchymyth and @sterndata).

The final code, which works, looks like this:

add_filter( 'body_class', 'custom_class' );
function custom_class( $classes ) {
    if ( is_tag() && !is_paged() ) {
        $classes[] = 'home-tag';
    } elseif ( is_category() && !is_paged() ) {
			  $classes[] = 'home-category';
		} elseif ( is_page_template('all.php') && !is_paged() ) {
			  $classes[] = 'home-paged';
		} else {
			
		}
    return $classes;
}

Thanks,