All the above is more relevant (but not strictly limited to) small prop twins. In a typical modern jet transport aircraft, once the engine failure is under control, then the aircraft is flown wings level, using rudder as appropriate. The result will be a small sideslip.
Interesting. I've never flown a jet, let alone a "modern jet transport aircraft". Why the difference? Why fly it wings level? Because you
can? For the better balancing of the G&Ts in the back? Or are there other issues?