Tesla use different systems for visualisation of traffic data and navigation routing. Navigation routing is always available and part of package, traffic visualisation is part of premium connectivity package that costs £9.99/month after the trial period, 1 or 12 months depending on the car.
Personal experience is that visualisation often shows traffic where there is none, even late at night. Its routine to come across an empty junction and visualisation showing it as slow traffic.
Navigation seems to do a fair job of taking traffic into account, but as its not linked to visualisation, you often do not know why its taken a preference for a particular route.
Only use for me for visualisation has been when getting stuck in a motorway jam and wanting to get a rough idea of how long it is. When there was a threat of us losing premium connectivity (long story affecting early adopters), I must admit I would have missed the live visualisations even though I don't trust them with any accuracy. But I wouldn't have paid £9.99/month for it.
My impression is that Tesla traffic updates are a bit behind what appears on your phone but by single digit minutes rather than anything longer. My previous car had live traffic but that was often out by 30+ mins vs checking Google Maps on your phone.
I believe the traffic data the car gets is via Google but not 100% sure on that.
It's always been identical to Google maps that I've seen. Yes it offers to re-route, you can specify the number of minutes saving for it to do it.
In terms of visualization it's pretty much an auto zooming map, you don't get quite as obvious information on which lane to be in, and the directions woman is terrible at counting exits on roundabouts for some reason. No speed camera warnings btw.
You won't bother using Google Maps instead. I know people who love using Waze and driving down residential streets to no perceptible benefit don't like it.
It seems to me that energy saving is part of the route calculation. I often have Apple nav running in parallel. Tesla will usually opt for the, slightly, slower more trafficy route compared to Apple. If I follow Apple the battery usage is often higher than when using Tesla nav.