To do that you need to edit two templates in your child theme, templates\single-product\pay.php (remove all lines except if with // Exit if accessed directly ) and templates\loop\pay-button.php – also remove all except that if statement.

Templates should go to your-child-theme\woocommerce\single-product\pay.php and your-child-theme\woocommerce\loop\pay-button.php

There is also pay button if user watches auction and ajax check is enabled, this one needs to be hidden using CSS:

.product-type-auction a.button {display: none}

add_filter( 'competitions_for_woocommerce_generate_random_ticket_numbers', 'custom_sequential_ticket_numbers', 10, 3 );
function custom_sequential_ticket_numbers( $random_tickets, $product_id, $qty ) {
    $available_tickets = competitions_for_woocommerce_get_available_ticket( $product_id );
    if ( empty( $available_tickets ) ) {
        return $random_tickets;
    }
    sort( $available_tickets );
    $sequential_tickets = array_slice( $available_tickets, 0, $qty );
    return $sequential_tickets;
}

add_filter( 'woocommerce_competition_my_tickets_endpoint_post_ids_active', 'my_custom_woocommerce_competition_my_tickets_endpoint_post_ids_active' );
add_filter( 'woocommerce_competition_my_tickets_endpoint_post_ids_past', 'my_custom_woocommerce_competition_my_tickets_endpoint_post_ids_past' );

function my_custom_woocommerce_competition_my_tickets_endpoint_post_ids_active() {

	$limit = 1;
	$current_user_id = get_current_user_id();
	$postids         = competitions_for_woocommerce_get_user_competitions();
	$posts_ids       = array();

	if ( count($postids)>0 ) {

		$args = array(
			'posts_per_page' => $limit,
			'fields' => 'ids',
			'post_type'=> 'product',
			'post__in' => $postids,
			'show_past_competitions' => false,
			'tax_query' => array( array('taxonomy' => 'product_type' , 'field' => 'slug', 'terms' => 'competition') ),
		);

		$the_query = new WP_Query( $args );
		$posts_ids = $the_query->posts;
	}
	$the_query = new WP_Query( $args );
	$posts_ids = $the_query->posts;

    return $posts_ids; // Always return the content, whether modified or not.
}


function my_custom_woocommerce_competition_my_tickets_endpoint_post_ids_past() {

	$limit = 1;
	$current_user_id = get_current_user_id();
	$postids         = competitions_for_woocommerce_get_user_competitions();
	$posts_ids       = array();

	if ( count( $postids ) > 0 ) {
		// Return past user's competition products.
		$args = array(
			'fields' => 'ids',
			'post_type'=> 'product',
			'post__in' => $postids,
			'show_past_competitions' => true,
			'meta_query' => array(
				array(
						'key' => '_competition_closed',
						'operator' => 'EXISTS',
					),
				),
		);

		$the_query = new WP_Query( $args );
		$posts_ids = $the_query->posts;
	}

    return $posts_ids; // Always return the content, whether modified or not.
}

add_filter( 'auctions_for_woocommerce_proxy_bid_to_reserve' , '__return_false', 20, 3 );

function custom_enqueue_script() {
    $product = wc_get_product( get_the_ID() );
    if ( $product && $product->get_type() == 'auction') {
        wp_add_inline_script( 'wd-woocommerce-quantity', 'jQuery(document).ready(function($) { woodmartThemeModule.$document.off("click", ".plus, .minus"); });');
    }
}
add_action( 'wp_enqueue_scripts', 'custom_enqueue_script', 999 );

add_filter( 'woodmart_ajax_add_to_cart', 'wpi_remove_add_ajax_to_cart', 10 );
function wpi_remove_add_ajax_to_cart ( $data ){
    $product  = wc_get_product( get_the_ID() );
    if ( is_product() ){
        if ( $product && $product->is_type('auction') ){
            return false;
        }
    }
    return $data;
}

form.auction_form.cart {
    margin: 15px 0;
}

.auction_form .quantity .qty {
    width: 250px !important;
}

input.plus {
    left: 250px;
}
input.minus {
    right: 250px;
}

button.bid_button.button.alt {
    flex: unset;
    left: 355px;
}

.auction_form.cart div.quantity {
     width: auto !important;
    border: none;
    margin: 0 10px 0 0 !important;
    position: initial !important;
    opacity: 1 !important;
    visibility: visible !important;
    pointer-events: initial !important;
    float:left !important;
}

.auction_form .quantity.buttons_added {display: block !important; visibility: visible !important;}

input.input-text.qty.bid.text.left  {display: inline}

.quantity.buttons_added {display: contents}

input.plus, input.minus,button.bid_button.button.alt {
    width: 40px;
}

button.bid_button.button.alt {
    margin: 0 0 0 10px;
}

add_filter( 'auctions_for_woocommerce_pay_now_button' , 'custom_auctions_for_woocommerce_pay_now_button', 10);
function custom_auctions_for_woocommerce_pay_now_button( $data ){
    global $product;
    if ( ! $product ) {
        return $data;
    }
    return esc_url( add_query_arg( 'pay-auction', $product->get_auction_id(), wc_get_cart_url() ) );
}
add_filter( 'auctions_for_woocommerce_pay_auction_redirect' , 'custom_auctions_for_woocommerce_pay_auction_redirect', 10);
function custom_auctions_for_woocommerce_pay_auction_redirect( $data ){
    return esc_url( remove_query_arg( array( 'pay-auction', 'quantity', 'product_id' ), wc_get_cart_url() ) );
}

add_action( 'template_redirect', 'afw_add_won_auctions_to_cart', 10 );
function afw_add_won_auctions_to_cart() {
    if ( ! is_admin() && is_user_logged_in() ) {
        $user_id = get_current_user_id();
        $auction_visibility_terms  = wc_get_auction_visibility_term_ids();
        $product_visibility_in     = array( $auction_visibility_terms['sold'] );

        $args    = array(
            'post_type'          => 'product',
            'posts_per_page'     => '-1',
            'meta_query'         => array(
                array(
                    'key'   => '_auction_current_bider',
                    'value' => $user_id,
                ),
                array(
                    'key'     => '_auction_payed',
                    'compare' => 'NOT EXISTS',
                ),

            ),
            'tax_query' => array(
                    'taxonomy' => 'auction_visibility',
                    'field'    => 'term_taxonomy_id',
                    'terms'    => $product_visibility_in,
                    'operator' => 'IN',
            ),
            'show_past_auctions' => true,
            'auction_arhive'     => true,
            'fields'                 => 'ids',
            'no_found_rows'          => true,
            'update_post_meta_cache' => false,
            'update_post_term_cache' => false,
        );

        $won_auctions = new WP_Query( $args );

        $posts_ids = $won_auctions->posts;

        if ( is_array( $posts_ids ) ) {

            foreach ( $posts_ids as $posts_id ) {

                $found = false;

                $product = wc_get_product( $posts_id );

                // check if auction ended and has highest bidder

                if ( is_object( WC()->cart ) && is_object( $product ) && method_exists( $product, 'get_auction_closed' ) && method_exists( $product, 'get_auction_payed' ) && ! $product->get_auction_payed() && 2 == $product->get_auction_closed() && ( $product->get_stock_quantity() > 0 ) ){

                        // check if already in cart

                        if ( sizeof( WC()->cart->get_cart() ) > 0 ) {

                            foreach ( WC()->cart->get_cart() as $cart_item_key => $values ) {
                                $_product = $values['data'];
                                if ( $_product->get_id() == $posts_id ) {
                                    $found = true;
                                }
                            }

                            if ( ! $found ) {
                                WC()->cart->add_to_cart( $posts_id );
                            }

                        } else {
                            WC()->cart->add_to_cart( $posts_id );
                        }



                }
            }
        }
    }
}

function afw_action_woocommerce_shortcode_products_loop_no_results( $attributes ) {
    echo __( 'No auction(s) found.', 'my-custom-language-domain' );
}
add_action( 'woocommerce_shortcode_ending_soon_auctions_loop_no_results', 'afw_action_woocommerce_shortcode_products_loop_no_results', 10, 1 );
add_action( 'woocommerce_shortcode_all_user_auctions_loop_no_results', 'afw_action_woocommerce_shortcode_products_loop_no_results', 10, 1 );

For ending_soon_auctions shortcode hook is woocommerce_shortcode_ending_soon_auctions_loop_no_results, in general hook is woocommerce_shortcode_[shortcode_name]_loop_no_results. This is applicable for both Auctions for Woo and Competitions for Woo plugins.