Step back in time indeed.
This was all I knew when I was growing up in Ireland and the UK. It is cooler there. For really bad weather we had sou'westers also but I never wore one. My cape was an oilskin, oiled cotton as the Carradice, but yellow. There were thumb loops so that the wind never blew it up over your head or even the handlebars. You could go all day in it and remain warm. Riding in a steady bunch you could maintain about 30kph but on your own you would be struggling to go that fast as there is considerable wind resistance. The oilskin was replaced by plastic, probably polyethelene or PVC. I still have one of those. The oilskin was not completely waterproof but breathed and leaked slightly where your body, usually just the arms touched the fabric. This was because touching the fabric broke the surface tension which was what made it waterproof. The plastic never leaked but was too hot to wear in Melbourne except on the coldest days.
The oiled cotton was similar to oiled Japara which bush jackets are made from, or at least were until modern fabrics arrived.
The best quality capes were made from oiled silk and had a ventilated back, not unlike a Driza-Bone. They were phenomenally expensive, relatively. I could never afford one.
Without doubt they are excellent to wear while pootling about but I would not choose to wear one on a long ride in Melbourne especially on a windy day. Today would have been a good day though. If you have mudguards or even cruds you do not needs spats though you will end up with damp feet probably, but if you are wearing business trousers, then you must get the spats.
To carry the cape when it was not raining, we just rolled it up and fastened it on top of our saddle bags or under the saddle.
The hardmen, hard riders and the racing boys never used a cape but had a variety of padded combat jackets which kept you warm and dry and did not have the same wind resistance. They were also cheaper (than capes) and you could get them from army disposal stores. Coupled with lambskin mittens, you could brave the arctic winds snow and sleet and arrive home feeling good.
In Melbourne I survive with the lightest of rain jackets and use many layers to keep warm in winter. I have not wanted to use a cape in years.
Stay fixed. Keeping a cool head.