@Arcana unlikely. the message this screenshot shows as being from 3 minutes ago was posted yesterday at 19:10 utc:
https://web.archive.org/web/20240112192756/https://www.nytimes.com/live/2024/01/11/world/israel-hamas-houthi-yemen-news

which means the screenshot was taken at 19:13 utc. the article in question already had the same summary it does now earlier than that, at 18:46 utc:
https://web.archive.org/web/20240112184617/https://www.nytimes.com/2024/01/12/world/europe/mideast-war-israel-yemen.html

it’s had it since before it was first placed on the main page somewhere between 18:47 utc and 18:54 utc:
https://web.archive.org/web/20240112184700/https://www.nytimes.com/
https://web.archive.org/web/20240112185438/https://www.nytimes.com/

i'm not sure why the new york times would be using an ai from a company they're suing to revise a perfectly acceptable human-written summary at least half an hour later than it was originally published