American in Norway here. The amount excluded depends on the tax treaty and is different for each country. Right now, if you make above around 100k USD in Norway (adjusted each year for inflation), that amount above is taxed by the US. But, that is only for regular employment.

If, for example, you decide to start freelancing, you still have to pay all of your self-employment taxes to the US, on top of the similar taxes here, even if your income is well below 100k.

Also, if you decided to start a company or start-up (i.e., anything that is not a sole proprietorship), you get into a hell hole of other compliance regulations that makes it VERY expensive. It effectively mean no one wants to cofound with you or invest in you. Having US citizenship while abroad is terrible for entrepreneurs. (source: conversations with other Americans who have tried and failed to launch startups here for these reasons)