The data is already available via Google's Chrome User Experience Report. It's comprised of PageSpeed Insights data from live users (those who have opted in to share such data), so it's aggregated across thousands of users, and is stored in a Google BigQuery database.
If you follow the link above, it documents all the key metrics that are available (with links to full explanations of each), as well as how to access the data. Unfortunately, I haven't had time to research the details, but I suspect your brain will light up immediately when you start reading.
I started this topic by requesting a new Connector and / or new functions. However, you might simply be able to update the PageSpeed Insights Connector, because I understand the Web Vitals metrics are now part of that. The specific Web Vitals metrics I'm most interested in are Largest Contentful Paint (LCP), First Input Delay (FID) and Cumulative Layout Shift (CLS). It's my understanding that these are going to be important pillars to the upcoming Page Experience update to Google's core algo that's coming in May 2021.
Hope this helps! As always, thanks for such a great product and for all your help!