I have no doubt that local agencies are screwing up the law, which is very new, but in Illinois "ALPR information" means information gathered by an ALPR or created from the analysis of data generated by an ALPR (everything after the quotation marks is a straight excerpt of the statute), and is confidential.
Do not get me started on small public bodies screwing up FOIA.
I'll assume you're correctly citing the statute — someone entering a sequence of characters in a "Search" field doesn't mean that the search term was "gathered by" or "created from the analysis of" ALPR data.
The search logs are public record even when alpr data is not; quite a few come from IL.