CustomAlgoliaEngine.php

<?php
namespace App\Engines;

use Laravel\Scout\Engines\AlgoliaEngine;
use Log;

class AdvancedAlgoliaEngine extends AlgoliaEngine
{
    protected $index;

    /**
     * Update the given model in the index.
     *
     * @param  \Illuminate\Database\Eloquent\Collection  $models
     * @throws \AlgoliaSearch\AlgoliaException
     * @return void
     */
    public function update($models)
    {
        foreach ($models as $model) {
            // We need to get the index for each model, because it can change
            $index = $this->algolia->initIndex($model->searchableAs());
            $array = $model->toSearchableArray();

            try {
                $algoliaObject = $index->getObject($model->getKey());

                // If we have changes, and $array ($model) is not empty, we update
                if ($this->arrayRecursiveDiff($array, $algoliaObject) && !empty($array)) {
                    array_merge(['objectID' => $model->getKey()], $array);
                    $result = $index->saveObject(
                        $array
                    );
                }

            } catch (\Exception $e) {
                if ((int)$e->getCode() == 404) {

                    // It gives error when doesn't exist, so if error we update (add)
                    array_merge(['objectID' => $model->getKey()], $array);

                    $result = $index->addObject(
                        $array
                    );

                } else {
                    Log::warning('Error was: ' . print_r($e, true));
                }
            }

        }
    }
                

    /**
     * Get the difference of arrays recursively
     *
     * @param array $aArray1
     * @param array $aArray2
     * @return array
     */
    function arrayRecursiveDiff($aArray1, $aArray2) {
        $aReturn = array();

        foreach ($aArray1 as $mKey => $mValue) {
            if (array_key_exists($mKey, $aArray2)) {
                if (is_array($mValue)) {
                    $aRecursiveDiff = $this->arrayRecursiveDiff($mValue, $aArray2[$mKey]);
                    if (count($aRecursiveDiff)) { $aReturn[$mKey] = $aRecursiveDiff; }
                } else {
                    if ($mValue != $aArray2[$mKey]) {
                        $aReturn[$mKey] = $mValue;
                    }
                }
            } else {
                $aReturn[$mKey] = $mValue;
            }
        }
        return $aReturn;
    }


    /**
     * Remove the given model from the index.
     *
     * @param  \Illuminate\Database\Eloquent\Collection  $models
     * @return void
     */
    public function delete($models)
    {
        foreach ($models as $model) {
            $index = $this->algolia->initIndex($model->searchableAs());
            $index->deleteObject($model->getKey());
        }
    }
}

You have to remove some fields in MongoDB, _id for example.
Some tuning is needed in the model to unset some fields and avoid duplication