I don’t own vector, but I’m 99% sure you can’t connect it to the phone and record data. That’s not what Garmin connect is. As far as I’m aware, the garmin connect connection is purely for vector firmware updates.
You’d need a suitable bike computer or watch. Even just an old Edge 500 would work, which you should be able to get for cheap as chips. That will record the basic power data. But newer devices which upload via your phone/Bluetooth are so much more convenient than having to plug into a computer each time.
People above mentioned trainerroad. That’s what I use and at least vector 3 also broadcasts in Bluetooth so all phones should work. I have an ant+ only Power2max so am restricted to Samsung phones with ant+ built in to get it to work without phone adapters. There are many similar trainerroad alternatives too. They’ve just put their prices up, altho their podcast this week said they’re doing a week period to lock in old prices.
I’ve never used zwift, but from everything I’ve seen and everyone I’ve spoken to, the immersive aspect relies on a smart trainer. Personally, I just rather train with my own videos/music/podcasts, hence why I use trainerroad