So many things.
I only use the companion app if I intend to interact with the game - which admittedly is most of the time. If I'm doing a workout to follow a route, I might not bother, but mostly I'm going to want to text chat, use power-ups, give ride ons. When I'm racing I might use the map to see how far off my team mates are, or even message them in game - we tend not to discord unless it's a TTT, you can only take so much panting and whirring while you're trying to give your all.
You can activate a power up without the companion app. Do it directly on the screen, with either touch screen, mouse, or even the blimmin ATV remote.
Power ups do make a difference. But only if you use them at the right time! Feather will give you a reduced mass so only helps if you're climbing. The helmet will reduce your CDA- so is only really noticeable on a sprint. The van acts like you're in a draft so you should notice that wherever, unless you're already in someone's draft. If you're racing and the girl you're drafting drops a burrito you sure as hell notice that you're kicked out of her draft. From a gamification point of view you should always 'spend' your power ups as you may get the small or large + which gives bonus XP, and you can only pick up a new power up if your circle is empty.
The companion app needs a good solid connection to your WiFi, but then, so does Zwift. I don't suffer from drop outs, but our WiFi coverage is good, we have a mesh for just this reason.
I read a while ago that it was a deliberate strategy not to give much of a manual with Zwift to force users to interact with each other, by asking questions and sharing tips, or to ride around and test things out themselves. I'm not sure it's helpful this far down the line as there are so many 'end game' users that a lot of beginner questions get answered with the kind of piss-taking sarcasm that can be very off putting.