The Handlebars cache is called handlebars and is registered by default when installing and activating the extension. Its cache backend is not configured explicitly and therefore uses the default setting (database cache).

You can specify a different cache backend as follows:

# ext_localconf.php

if (!isset($GLOBALS['TYPO3_CONF_VARS']['SYS']['caching']['cacheConfigurations']['handlebars']['backend'])) {
        = \TYPO3\CMS\Core\Cache\Backend\SimpleFileBackend::class;

See also

Read more about cache configuration in the official TYPO3 documentation.