The good news Katy is that it's easier on an e-bike, at least I think so. The main issue I have with rainwear is over-heating, and on an e-bike you just never get as hot. That said I would recommend going for the lightest waterproof layer possible, because then you can use it all year round, and stick a fleece under it if it's really cold.
I've been through a variety of capes and ponchos and my conclusion is that you need arms for signalling and they don't really stay down over your legs unless weighted or held in place with elastic loops. If you sort that out and it's long enough, then it will keep your thighs dry but your lower legs and feet will still get wet. On an upright bike, the ones that drape over your handlebars allow a surprising amount of rain onto your legs.
I've just ordered a Georgia in Dublin rain skirt and the Leggits, because rain trousers are too much faff, especially if you cycle in civilian clothes and shoes and are not going to have to get changed at work. I'll let you know how I get on, but the skirt gets a good write-up here . I've been eyeing the skirt suspiciously for a couple of years, but I suspect it might be the answer, and I could do with a picnic blanket anyway.
In response to your other thread, which I was a bit late for, the answer is you can easily cycle every day, especially in East Anglia which gets hardly any rain 
. I've realised that actually cycling makes a rainy day better rather than worse, but that might just be me!