I use a bike poncho, it covers the legs, too, and limits sweating because it is open underneath. Decathlon sells them for cheap, and them works. There is also normal colors, but I prefer to be absurdly visible (I want to see who says "I didn't seen him 🙂)
Every time I use it, I'm amazed I'm dry underneath (the face gets wet).
In any case, even if I don't wear it, I'm unlikely to get soaked, when rain is not that strong. We are not made of sugar!
crosspostated from: https://social.tchncs.de/users/lgsp/statuses/115484700218126774
you also need water proof pants/shoes/socks. and really good fenders on your bike. most bikes do not have fenders.
covering your upper body is ok in light rain maybe, not not in significant rain.