Custom Label : Fetch all Custom Label Information through Execute Anonymous Script

CustomLabel is available in Tooling API and can be used to get all CustomLabel Information. With single callout, REST API return 2000 records and then provide "nextRecordsUrl" attribute which contain URI for next set of custom label.

If you want to create class in your org and execute it methods to get custom label information, then refer below URL:

Custom Label : Fetch all Custom Label Information using Tooling API

But if you don't want to deploy new class to production or any org to get custom label information, then you can run below apex script in execute anonymous window in developer console to get custom label information.

Hope this will help!!!