What is the user agent of the crawler, which delivers Core Web Vitals data into Google Search Console?
I can't find any info about, whether it is the same crawler of PageSpeed Insight, as discussed here, or is it another crawler with different user agent?
There is no user agent for Core Web Vitals as the vitals are directly gathered from within Chrome. So basically all your visitors using a Chrome browser are checking your website and anonymously sending that data to Google.
This is called CrUX data and that is what is displayed in Google Search Console, the live field data.
No bot/crawler involved in this process.