I assume they mean 400k net, if the employer pays 413k you only get 206k after tax. While the tax burden seems huge in this case, it's not that different in the US, though. For example you'd get around 225k in California (with no deductions).

Yes, if you get 400k gross, your employer has to pay 413k, but you only get 221k net after deduction of taxes and obligatory insurances (according to that very same calculator).

no engineer makes 400k a year in Germany. This is not the US, sadly.

"net" is the keyword here.