Populate l10n_state field of tt_content records when creating a translation. So the radio buttons for allowLanguageSynchronization are set to 'custom value' by default.

DataHandler.php

<?php

namespace Some\Client\Hooks;

/**
 * DataHandler
 *
 * Contains hooks for the \TYPO3\CMS\Core\DataHandling\DataHandler class
 */
class DataHandler
{
    /**
     * Populate l10n_state field of tt_content records when creating a translation. So the radio buttons for
     * allowLanguageSynchronization are set to 'custom value' by default.
     *
     * @param \TYPO3\CMS\Core\DataHandling\DataHandler $dataHandler
     */
    public function processDatamap_beforeStart(\TYPO3\CMS\Core\DataHandling\DataHandler $dataHandler): void
    {
        if (empty($dataHandler->datamap['tt_content'])) {
            return;
        }
        foreach ($dataHandler->datamap['tt_content'] as $id => $record) {
            if (strpos($id, 'NEW') === false) {
                continue;
            }
            $l10n_state = '{"image": "custom"}';
            if ($record['l10n_state']) {
                $defaultState = json_decode($record['l10n_state'], true);
                $defaultState['image'] = 'custom';
                $l10n_state = json_encode($defaultState, JSON_FORCE_OBJECT);
            }
            $record['l10n_state'] = $l10n_state;
            $dataHandler->datamap['tt_content'][$id] = $record;
        }
    }
}