Daily face wash - what do you use for dry skin?

[Waterdrinker]

Hello lovely ladies! I need some skincare advice. I have really dry skin on my face. For a good couple of months, I used this face wash everyday and it made my dry skin even worse. I do moisturise my face after every shower.
I don't wear make-up.
I would like suggestions on how to clean my face everyday- I don't want to buy any more face washes. I just saw this online - Cetaphil Hydrating Foaming Cream Cleanser Face Wash.
Would this cream cleanser NOT dry out my skin?
I honestly don't know what to use on my face. When I was a kid/teenager, I used to use old-fashioned soap on my face and had no problems.

Things you need to wash off your face aside from make up and dust:

Sweat

Sebum (oil from your sebaceous glands)

Dead skin cells from you and your partner/pets/children/anything else that shares your bed.

and at night: sunscreen which obviously everyone wears every day all year round (!)

Dust is the dead skin cells etc; sweat comes off with a bit of water and a rub with a hand or cloth, not like a face gets smelly like armpits; having dry skin means I need to hold onto what little oil my skin may be producing.
Most products irritate my skin in some way, a splash of water and some moisturiser have done me well so far and I’m not filthy and my skin looks fine.
I don’t wear sunscreen in winter, sadly not able to be outside much and don’t see the point for approx 10-20 mins total of being outside on a grey rainy day 🤷‍♀️