Think mine was from Aldi ages ago, pretty similar to what Assos offer so it’s just a shower proof shell. It’s called a ‘race cape’ Decathlon do some super lightweight running jackets that are a slim fit – used to have one but lost it! Both of these fold(ed) up small to stick in the back pocket.
How often are you out on the road? I can’t actually remember the last time I needed to wear mine, so maybe shy away from spending too much (unless you want to of course).
Decent (not crud/mtb flinger type) full mudguards are more essential than a jacket, providing you’re wearing enough layers for the temperature of course!