How to extend tag and category “Related Posts” query to custom post_type if the first 2 terms have no posts

You should take your third query outside the first

// We will now run the second query if $count is less than $total_posts
if ( $count < $total_posts ) {

condition. You should also need to update the counter after the second query and rebuild the list to exclude posts already in the array of ID’s. We al use the same logic as we have used in the first query to run the third one.

I have just copied my code over from my answer here and extended it. Again, this is untested, so it might be buggy. Use case stays exactly the same

function get_max_related_posts( $taxonomy_1 = 'post_tag', $taxonomy_2 = 'category', $total_posts = 4 )
{
    // First, make sure we are on a single page, if not, bail
    if ( !is_single() )
        return false;

    // Sanitize and vaidate our incoming data
    if ( 'post_tag' !== $taxonomy_1 ) {
        $taxonomy_1 = filter_var( $taxonomy_1, FILTER_SANITIZE_STRING );
        if ( !taxonomy_exists( $taxonomy_1 ) )
            return false;
    }

    if ( 'category' !== $taxonomy_2 ) {
        $taxonomy_2 = filter_var( $taxonomy_2, FILTER_SANITIZE_STRING );
        if ( !taxonomy_exists( $taxonomy_2 ) )
            return false;
    }

    if ( 4 !== $total_posts ) {
        $total_posts = filter_var( $total_posts, FILTER_VALIDATE_INT );
            if ( !$total_posts )
                return false;
    }

    // Everything checks out and is sanitized, lets get the current post
    $current_post = sanitize_post( $GLOBALS['wp_the_query']->get_queried_object() );

    // Lets get the first taxonomy's terms belonging to the post
    $terms_1 = get_the_terms( $current_post, $taxonomy_1 );

    // Set a varaible to hold the post count from first query
    $count = 0;
    // Set a variable to hold the results from query 1
    $q_1   = [];

    // Make sure we have terms
    if ( $terms_1 ) {
        // Lets get the term ID's
        $term_1_ids = wp_list_pluck( $terms_1, 'term_id' );

        // Lets build the query to get related posts
        $args_1 = [
            'post_type'      => $current_post->post_type,
            'post__not_in'   => [$current_post->ID],
            'posts_per_page' => $total_posts,
            'fields'         => 'ids',
            'tax_query'      => [
                [
                    'taxonomy'         => $taxonomy_1,
                    'terms'            => $term_1_ids,
                    'include_children' => false
                ]
            ],
        ];
        $q_1 = get_posts( $args_1 );

        // Update our counter
        $count = count( $q_1 );
    }

    // We will now run the second query if $count is less than $total_posts
    if ( $count < $total_posts ) {
        $terms_2 = get_the_terms( $current_post, $taxonomy_2 );
        // Make sure we have terms
        if ( $terms_2 ) {
            // Lets get the term ID's
            $term_2_ids = wp_list_pluck( $terms_2, 'term_id' );

            // Calculate the amount of post to get
            $diff = $total_posts - $count;

            // Create an array of post ID's to exclude
            if ( $q_1 ) {
                $exclude = array_merge( [$current_post->ID], $q_1 );
            } else {
                $exclude = [$current_post->ID];
            }

            $args_2 = [
                'post_type'      => $current_post->post_type,
                'post__not_in'   => $exclude,
                'posts_per_page' => $diff,
                'fields'         => 'ids',
                'tax_query'      => [
                    [
                        'taxonomy'         => $taxonomy_2,
                        'terms'            => $term_2_ids,
                        'include_children' => false
                    ]
                ],
            ];
            $q_2 = get_posts( $args_2 );

            if ( $q_2 ) {
                // Merge the two results into one array of ID's
                $q_1 = array_merge( $q_1, $q_2 );

                // Update our post counter
                $count = count( $q_1 );
            }
        }
    }

    // We will now run the third query if $count is less than $total_posts
    if ( $count < $total_posts ) {
        // Calculate the amount of post to get
        $diff = $total_posts - $count;

        // Build an array of posts to exclude
        if ( $q_1 ) {
            $exclude = array_merge( [$current_post->ID], $q_1 );
        } else {
            $exclude = [$current_post->ID];
        }

        $args_3 = [
            'post_type'      => $current_post->post_type,
            'post__not_in'   => $exclude,
            'posts_per_page' => $diff,
            'fields'         => 'ids',
        ];
        $q_3 = get_posts( $args_3 );

        if ( $q_3 ) {
            // Merge the two results into one array of ID's
            $q_1 = array_merge( $q_1, $q_3 );
        }
    }

    // Make sure we have an array of ID's
    if ( !$q_1 )
        return false;

    // Run our last query, and output the results
    $final_args = [
        'ignore_sticky_posts' => 1,
        'post_type'           => $current_post->post_type,
        'posts_per_page'      => count( $q_1 ),
        'post__in'            => $q_1,
        'order'               => 'ASC',
        'orderby'             => 'post__in',
        'suppress_filters'    => true,
        'no_found_rows'       => true
    ];
    $final_query = new WP_Query( $final_args );

    return $final_query;
}