Generally, information recorded (or maintained by, and often if contracted through a third party) by a government agency is made public if that state's public records law does not consider it to be private. "Private" is usually defined on a state-by-state basis. Every state has a public records law.

Some states consider license plates to be private, while others don't. Foe example, Illinois considers license plates private only if it's associated with other personally associatable information.

Aggregate or redacted information on accidents might be accessible in the case of privacy exemptions. Unless it's all on paper, which dramatically complicates things because of the efforts required to review/redact where needed.

In other words - if an agency has access to records on traffic incidents, it's probably accessible.

Around here there would be a public record of an accidents location if it was big enough to bother waiting for the police, although the public portion of that would not be tied to my name or license plate. Announcements (by authorities) on larger accidents mostly contain maybe an age, gender, and generic vehicle information. Other than that only the two insurances involved would get more data.

The only thing I could think of that made more information public might be lawsuits that could occasionally result from an accident but I'm not sure on how public those currently are. Our news around here usually refrain from naming people in reporting anyway if it's not too relevant or it's a public person anyway.

If there's a police report, then of course it's a public record.

In the EU, the "e-Call" system is being rolled out which mandates that the car automatically phones home in the event of a crash: https://en.wikipedia.org/wiki/ECall