<?php
add_filter( 'woocommerce_add_to_cart_validation', 'limit_product_quantity_in_cart', 10, 3 );
function limit_product_quantity_in_cart( $passed, $product_id, $quantity ) {
    if ( $quantity > 1 ) {
        wc_add_notice( __( 'Only a quantity of one is allowed per product.', 'domain' ), 'error' );
        return false;
    }
    foreach ( WC()->cart->get_cart() as $cart_item ) {
        if ( $cart_item['product_id'] == $product_id || ( isset( $cart_item['variation_id'] ) && $cart_item['variation_id'] == $product_id ) ) {
            wc_add_notice( __( 'This product is already in your cart. Only a quantity of one is allowed per product.', 'domain' ), 'error' );
            return false;
        }
    }
    return $passed;
}