Yes power is a rate. As you said energy is the time integral of power. So it’s meaningless to state an “energy draw” without a duration implied or explicit. E.g. what does drawing 2kWh at idle even mean?
I agree about end user sentiment. I was trying to suggest as well. The only way to know which battery/phone is going to have a better battery life is to identify reviews with similar usage to your own or cross-compare metrics across devices you’re familiar with. In general, phone A with a 4000mAh battery won’t necessarily outlast phone B with a 4500mAh batt.
Per the kW vs kWh, see top level reply.
Yeah a metric would be nice but it would need a standard test. That’s why idle time and video playback time makes a good amount of sense. But it’s not entirely clear how that would translate into usage for example in back country (where cell network drains power harder) or travel. So it’s not perfect. But it is probably the best measure guven hardware and usage vatiation. In any case it’s subject to marketing dudging the numbers in various ways.