In my commuting to work and back days it was wellies for heavy rain. I would always have them with me rolled up in my panniers ready just in case.
In really heavy rain if it was not too cold I would in addition wear just my over trousers over my undies, and nothing under my wind proof cheap hi viz cycling jacket. I had one with an attachable hood which I attached. Also waterproof thermal gloves and a beanie style hat under the hood. Also a balaclava to cover you nose, mouth and neck tucked into the jacket.
I wore only my undies under the wind proof layers as although these windproof layers had been originally water proof, I found nothing stayed that way very long in an everyday commuting environment.
I always pedal my electric bikes hard enough to be exercise warm and this worked well as long as I wore wind proof layers and ensured my head, face and hands were covered.
I also use Ortleib panniers so that the layers I was not wearing would stay bone dry in my panniers and be ready to use the next day.
At home my wind proof layers would dry very quickly in my boiler/drying cupboard and be ready for the next days commute. Likewise the beanie, gloves and balaclava.
Other stuff worn under would just get wet, feel uncomfortable and not dry by the next day.
Of course under a certain temperature you need to wear more stuff! But a cold night usually meant a clear sky and no rain.
If you ride to work and back you need simple cheap solutions that just work.