Apparently there is scraping of public data + keyword matching + moderators filtering the matches.
An example that he shows a bit earlier in the video comes from this page, which has an RSS feed: https://www.cityofsanbenito.com/AgendaCenter/City-Commission...
The video says it's open source but I can't find the source.
I also gave a talk on this concept that walks through the whole process: https://www.youtube.com/watch?v=MtWzNnZvQ6w
The short answer is: there's no common API for any of these sites, and even the ones that do have an API are sometimes misconfigured. It's why I wrote all the scrapers by hand.