Override Product Price Programmatically

Hi,

I added some code for annual billing & monthly billing by radio button selection. My code is working both on cart & checkout page. But by applying my code , other pages of website are not working
Please check my code:-

add_action( 'woocommerce_review_order_before_payment', 'checkout_radio_choice' );
  
function checkout_radio_choice() {
     
   $chosen = WC()->session->get( 'radio_chosen' );
   $chosen = empty( $chosen ) ? WC()->checkout->get_value( 'radio_choice' ) : $chosen;
   $chosen = empty( $chosen ) ? '0' : $chosen;
        
   $args = array(
   'type' => 'radio',
   'class' => array( 'form-row-wide', 'update_totals_on_change' ),
   'options' => array(
      '0' => 'Monthly Billing',
      '10' => 'Annual Billing',
      
   ),
   'default' => $chosen
   );
     
   echo '<div id="checkout-radio">';
   echo '<h5>Billing Option</h5>';
   woocommerce_form_field( 'radio_choice', $args, $chosen );
   echo '</div>';
     
}

   
add_action( 'woocommerce_get_price_html', 'checkout_radio_choice_fee', 9999, 2 );
  
function checkout_radio_choice_fee( $cart ) {

   $orig_price = wc_get_price_to_display( $product );
   if ( is_admin() && ! defined( 'DOING_AJAX' ) ) return;
    
   $radio = WC()->session->get( 'radio_chosen' );
    if ( $radio == "10") {
$orig_price = wc_get_price_to_display( $product );
$price_html = wc_price( $orig_price*12 ); 

 }
else{  
$orig_price = wc_get_price_to_display( $product );
$price_html = $product->get_price();
 
 }
   return $price_html;
}
add_action( 'woocommerce_before_calculate_totals', 'alter_price_cart', 9999 );
 
function alter_price_cart( $cart ) {
 
    if ( is_admin() && ! defined( 'DOING_AJAX' ) ) return;
 
    if ( did_action( 'woocommerce_before_calculate_totals' ) >= 2 ) return;
 
   $radio = WC()->session->get( 'radio_chosen' );
 
  
    foreach ( $cart->get_cart() as $cart_item_key => $cart_item ) {
 
    if ( $radio == "10") {
        $product = $cart_item['data'];
        $price = $product->get_price();

        $cart_item['data']->set_price( $price *12 );}
else{   $product = $cart_item['data'];
        $price = $product->get_price();

        $cart_item['data']->set_price( $price);exit;}

}

 
}

  
add_action( 'woocommerce_checkout_update_order_review', 'checkout_radio_choice_set_session' );
  
function checkout_radio_choice_set_session( $posted_data ) {
    parse_str( $posted_data, $output );
    if ( isset( $output['radio_choice'] ) ){
        WC()->session->set( 'radio_chosen', $output['radio_choice'] );
    }
}

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