chronicgraph What identifiers can possibly connect the profiles together?
https://github.com/GrapheneOS/os-issue-tracker/issues/2314
Also, behavioral features of the hardware can in theory be aggravated into a probabilistic identifier. Each device's time-of-day clock runs at a different rate. That is corrected by NTP, but the corrections are observable. Two profiles on a device may "wake up" and "go to sleep" at roughly the same time on any given day, when the human driver of both wakes up and goes to sleep.
chronicgraph Is making a new profile and using a vpn equivalent to getting a totally separate burner device?
No.
A truly determined party can make use of covert channels. For example, because the device has one storage pool, in theory an app in one profile could create and delete junk files of a specific size with specific timing and an app in a different profile could observe how much space is free. Timed usage pulsing of CPU could be done as well.
Two profiles on one device are factually on one device, and it's hard to completely hide true facts from a determined party who "lives with" you.
But meanwhile two different devices used by one person may eventually be correlated if behavioral clues are patiently accumulated over time.
Edit: The good news is that most parties don't try that hard, because plenty of people are happy to reveal their identities easily via ways that work instantly. But if somebody is willing to work hard and over time, scraps of information are leaked and can be assembled.