...do I get basically the same functionality from the Premium Connectivity streaming, which I have for free for a year?
No. Tesla Premium Connectivity is just like a generic internet provider and it does not cover your Spotify fee, Netflix fee, Amazon Prime Video fee...
You can't use Spotify app from your Tesla car unless you pay Spotify (no free Spotify version for your Tesla car).
Telsa does cover your
$3.99/month Slacker.com Plus for free whether you bought Tesla Premium Connectivity or not. If you bought Tesla Premium Connectivity, you can use Slacker while driving as well as parking. Without Tesla Premium Connectivity, you can only use its slacker.com app via a wi-fi (could be a stationary source like at home or a mobile wi-fi hotspot).
I didn't like Slacker.com because it lacked my favorite music for years since I first got a Tesla in 2012 while Spotify has had a big global selection.
Within a couple of years, the free Slacker. com app in your Tesla is pretty good in terms of expanding selection and should catch up with Spotify pretty soon.
So if you can afford a $2/month more for Spotify, I would go ahead.
If not, just use the included and rival and free Slacker.com app in your Tesla.