Figured it out.
It’s possible to pass the ‘sw-language-id’ Header with a specified language id.
Magic happens in \Shopware\Core\Framework\Routing\ApiRequestContextResolver::getRuntimeParameters
Some documentation would have been nice here.
Note that specified unique id of the langauge must follow the Regex in \Shopware\Core\Framework\Uuid\Uuid::VALID_PATTERN, otherwise some validation check fails.