I don't know the exact functionality of this extension and the interaction with the component flatpickr.js.

In my opinion, the most pragmatic way would be to consider the timezone just before accessing the persistence in BackendLogController::setStartAndEndTimeFromTimeSelector(). The following code is quick and dirty but achieves the expected result:

    protected function setStartAndEndTimeFromTimeSelector(Constraint $constraint)
    {
        $timezone = new \DateTimeZone(date_default_timezone_get());
        $startTime = $constraint->getManualDateStart()
            ? (new \DateTime(
                $constraint->getManualDateStart()->format('Y-m-d H:i:s'),
                $timezone
            ))->getTimestamp()
            : 0;
        $endTime = $constraint->getManualDateStop()
            ? (new \DateTime(
                $constraint->getManualDateStop()->format('Y-m-d H:i:s'),
                $timezone
            ))->getTimestamp()
            : 0;
        if ($endTime <= $startTime) {
            $endTime = $GLOBALS['EXEC_TIME'];
        }
        $constraint->setStartTimestamp($startTime);
        $constraint->setEndTimestamp($endTime);
    }