Most of the modern electric liners with arms attached, look like a windcheater. I use my RapidFire liner that way. I doubt if it’s waterproof, much beyond a very light shower. If you are really fussy, take a fleece * or one of those down jacket things that fold up or compress small. I have all three, but taking with me only what I think will be appropriate for my jaunt. None of them take up much room on the bike and I don’t have huuuuuge ‘must have’ panniers. Even an EDZ shell will do, if that’s your thing.
* Various thicknesses available and can be used as a layer on the bike, possibly dispensing with the need for anything electrical at all.
I use my Gerbing one as a jacket when I'm off the bike, it's like a soft shell jacket. The only downside is for a heated jacket to be effective it has to be a tight fit which isn't great when you are off the bike.