I think you got most of that right. But let me just go through those again and maybe clear up some things that way:
- Core Web Vitals are performance metrics. They do contribute to Performance Score in both PageSpeed Insights and Lighthouse, and these Performance Scores do change every now and then when it comes to weighting.
Core Web Vitals measured in the field (gathered from Chrome users that meet certain data sharing conditions) are stored in the CrUX database and that's the data Google is planning to use in search ranking. Performance Score doesn't play a role here.
Not every website will have the field data available in CrUX because there are certain traffic thresholds you need to meet to be included.
CrUX via BigQuery contains detailed origin-level data, but you can access page-level data via PSI API, CrUX API, or the CrUX Dashboard (I think? I haven't used that in ages)
- You can also simulate Core Web Vitals in a lab environment - a machine with predetermined connection speed and computing power opens up the page and measures the performance, including CWV. That's what you see in Lighthouse and PageSpeed Insights (although PSI also contains some field data from CrUX)
- Google Search Console shows a very high-level overview of CrUX data, yes.
- Again, haven't used it in ages but that seems correct.
The key thing to understand is the difference between lab and field data (
shameless plug here, sorry). Field data gives you a more real view of how your users experience your website while browsing, and it's what Google will use for search. BUT lab data is what you need to use when debugging, just because you can run a lab test on-demand and don't have to wait for the real user data to come in.
For reporting, you need to use whatever looks better ;p I'm assuming you mean reporting to the business side - field data is what ultimately represents your performance as seen by your users and will correlate well with business metrics, so as someone with business KPIs that's what I'd wanna see.