The act of searching a specific plate up in the government's database is a defacto search under the 4th Amendment as ruled repeatedly by SCOTUS. That the lower circuit courts ignore this (also repeatedly) doesn't change this fact.
SCOTUS has repeatedly stated that a private citizens movements while in public are considered private. Thus, public license plate readers are not actually legal under the 4th amendment. Lower level courts like to to do mental gymnastics to justify them, but at the SCOTUS level they are not legal.
For instance in 4th circuit appeals case, Schmidt v. City of Norfolk, the courts argued that with regards to fixed location license plate readers, that their "brief" and "non-continuous snapshots" of a vehicle on public streets, doesn't constitute a "search" under the 4th amendment. But in several other cases such as Carpenter v. United States (2018), SCOTUS has concluded that monitoring a persons movements, be it via camera, cell phone data, gps, etc. all constitute a "search" under the 4A and enjoy privacy protections.