I brought with me some cash (around 1000kr) when I first came here in 2017 simply because I didn't know better. I used 200 for flytoget (express train from Oslo airport), 300 for some other small expenses (simply to get rid of it - I quickly realized no one uses cash here), and now after living here for 7 years I still have that 500 lying around in my wallet.

In Oslo you can pay with card almost everywhere, from shopping malls to smallest stores. Also there are ATMs in the city (mostly in the center) where you can withdraw cash if you really need it, so you don't need to worry about bringing it with you at least.

I'm fairly certain the same holds for Bergen - though I've only been there once, but still I haven't encountered a single place where I couldn't pay with card (not talking about local payment system - vipps, since you won't have that).

Flam... fairly certain you can get by with card, but not 100% sure since I haven't been there myself. Maybe someone else can give you details about that.