Dates are actually stored as integers. The format options are for printing, not for storing the date values.
dt_test <- data.table(
date = as.Date(c("01.03.2019", "02.03.2019"), format = "%d.%m.%Y"),
value = c(1, 2))
You will have to define your desired date format when you want to display the date values, e.g. in your plots. You can use the format above or use lubridate.