How to derive a child’s private key, such as an electrum, by PHP?

You can actually use the Bitcoin-PHP library. The following features must work.

<?php

require "vendor/autoload.php";

use BitWasp\Bitcoin\Bitcoin;
use BitWasp\Bitcoin\Key\Deterministic\HierarchicalKeyFactory;
use BitWasp\Bitcoin\Network\NetworkFactory;
use BitWasp\Bitcoin\Serializer\Key\HierarchicalKey\ExtendedKeySerializer;
use BitWasp\Bitcoin\Serializer\Key\HierarchicalKey\Base58ExtendedKeySerializer;

// Function to derive private key from a given master private key and path
function getPrivateKeyFromPath($masterKey, $path) 
    $network = NetworkFactory::bitcoin(); // Change to testnet if needed

    // Deserialize the master key
    $serializer = new ExtendedKeySerializer(new Base58ExtendedKeySerializer(Bitcoin::getMath()));
    $hdFactory = new HierarchicalKeyFactory();
    $key = $serializer->deserialize($network, $masterKey);

    // Derive the child key for the given path
    $segments = explode("https://bitcoin.stackexchange.com/", trim($path, "https://bitcoin.stackexchange.com/"));
    foreach ($segments as $segment) 
        $index = intval($segment);
        $key = $key->deriveChild($index);
    

    return $key->getPrivateKey()->toWif($network);