To keep Atahualpa compatible with PHP 8.1 you should change the following:

in functions/bfa_ata_custom_comments.php to remove some notice level errors:
old: $comment = get_comment($comment_id);

$comment = get_comment($comment_id  ?? 0);

To remove warnings and in some cases a crash in functions.php
Remove the lines 858 to 863 - Internet Explorer 6 is long dead and there are some problems with this function. I don't think it would work anyhow so no reason in fixing it:

		if ($bfa_ata['pngfix_selectors'] != "" AND $isIE6 = TRUE) 
		{
			wp_register_script('ddroundies', $templateURI . '/js/DD_roundies.js', false, '0.0.2a' );
			wp_enqueue_script('ddroundies');
			add_action('wp_head', 'bfa_ddroundiesHead');
		}

As well as don't forget to remove line 107 (the closing ampersand) from js.php from version 3.7.26

I attach the 3 files below (cannot attach full version due to file size attachement restrictions):

I got the following notice to change for PHP 8.2 by another user Valentin F. (he is not registered here):

In css.php lines 137&138 i had to do an int cast because of this error:
PHP Fatal error: Uncaught TypeError: Unsupported operand types: string + int

Change from:

$bfa_ata['layout_min'] = $bfa_ata['layout_min_width'] + ( $bfa_ata['layout_style_leftright_padding'] * 2 );
$bfa_ata['layout_max'] = $bfa_ata['layout_max_width'] + ( $bfa_ata['layout_style_leftright_padding'] * 2 );

to:

$bfa_ata['layout_min'] = (int) $bfa_ata['layout_min_width'] + ( $bfa_ata['layout_style_leftright_padding'] * 2 );
$bfa_ata['layout_max'] = (int) $bfa_ata['layout_max_width'] + ( $bfa_ata['layout_style_leftright_padding'] * 2 );

I just updated to php 8.2 and it works flawless even though I have loads of plugins. Seem everyone done his homework by now (half a year ago upon release plenty was broken still on 8.2)