Nothing truly waterproof will ever breath very well. The best breathing 3-layer waterproof membranes right now are Polartec NeoShell, eVent, Gore-tex Pro or Active, or Dermizax NX . Look for a shell made of one of those three if you want best-in-class true waterproofness and limited breathability. Pit zips will help breath. This is fine for low-intensity activites but if you're cycling very hard or very long you will build up a bunch of sweat from the inside. Right now, thats just a fact of where the fabric science is.

My preferred of those is Derminzax (very hard to find) and eVent. The breathe a bit better than the others in my experience.

Other options would be a hybrid or softshell material -- better breathability with a good DWR treatment.

Or the cheapest option would be re-treating your current jacket with DWR to see if it can be restored. This won't keep you dry in a downpour, but it would be okay in less intense weather events.

Riding in a puffy would make me sweat instantly. And most puffy's *suck* at breathing (because they are made to be relatively wind resistant.) Something like a Patagonia Nano Air or a thick fleece is the typically preferred insulator for higher intensity activities because they breathe far better.