How do I use PHP to display the alt text in for a featured image

Yes you do need to fetch alt text first.
Check this question on stackoverflow: https://stackoverflow.com/questions/19267650/get-wordpress-featured-image-alt

Hope this helps.

It appears that you might be using Advanced Custom Fields.

If that is the case, I would look at their documentation regarding displaying images.

https://www.advancedcustomfields.com/resources/image/

If you set ACF to return the ID, you can then use

$image = get_field('page_featured_image');
$size = 'full'; // (thumbnail, medium, large, full or custom size)

if( $image ) {

	echo wp_get_attachment_image( $image, $size );

}

This is also good as can return a responsive srcset of images.