Out of the box, Tesla sends anonymized location data (the anonymization can't be perfect as the article points out) for traffic data reporting. Otherwise, pretty much every system in the car like the headlights, CAN bus, ABS, door and window microcontrollers, HVAC, battery management system, etc. are both updated during OTA updates, and send tons of telemetry to the main computer for processing and streaming to HQ, allowing Tesla to do extreme optimization and analysis on how well their parts are working and how efficient they are, with the ability to get cars in for service long before a problem turns into a catastrophic failure or makes the vehicle undriveable.
When I had to implement similar stuff in a program I created the user was Always prompted and the user had an easy way to check the data that was sent and they could deny sending the report.
I assume the car has enough computing power to self diagnose any component issue and you don't need to send your logs to the cloud for a super computer to see that your battery is broken. My guess is like all telemetry, it is done for the company benefit not the user.