So I tried to measure the page speed of a website of while doing website Improvements and found that the Core Web Vitals Assessment was showing as not applicable , it showed something like this - Core Web Vitals Assessment: Not Applicable
Except the first contentful paint (FCP), everything else was showing as N/A Core web-vitals screenshot
I tried the SOP of improving the page speed by considering various suggestions which displyed on the core web vitals on pagespeed.dev, after pondering on it for over a week, there was no change to the page speed or improvement to the website.
This suggests that your site is at the borderline of getting sufficient traffic to appear in CrUX. It just scrapes in for FCP data, but has no data for the other Core Web Vitals.
You can still get some actionable insights from the Lighthouse section of PageSpeed Insights, or can collect your own Core Web Vitals data using a RUM tool or the web-vitals JavaScript library.
You may also have some insights from the origin-level data, or for mobile if that data is available to you.