There are plenty of free android applications showing you your local cellular info with CID LAC, CI etc.
For example "Signal strength" APK. It's just matter of time until you will find one with logging and export ability. You can always write it down with pencil :)
Naw, this is HN, so it'd be more like take a screen shot, upload to some ML tool you cooked up in a weekend that OCRs the data, loads it into a NoSQL database with the cotnent presented in the latest fad JS framework using Lamda functions or some other cloud hosted CI/CD blue-green deployment to support both users.
As the essay notes, it's through TelephonyManager on Android. On iOS it used to be possible through CoreTelephony private APIs, but I think Apple cracked down on these a few years back and either removed them entirely or locked them down behind entitlements, as they were getting abused by analytics frameworks.