The LCP shown by Google Search Console is not incorrect

No, Google Search Console is not off the mark when it reports a poor LCP overall while individual pages seem fine. Barry Pollard explains that the difference comes from the way GSC and CrUX measure the Core Web Vitals.

CrUX calculates performance at the 75th percentile of page loads, which means that if more than 25% of page views are slower, the overall score drops. Popular pages, often shown as examples in GSC, have sufficient data and are generally faster because they benefit from caches (database, Varnish, CDN). Long-tail pages (less frequented), which can represent more than 25% of total traffic, are often not cached and therefore slower, even if they are technically identical. In addition, low-demand pages trigger “cache misses” and must be generated from scratch, increasing LCP.

Here are Philip Walton's tips to improve the situation :

• Measure performance without cache: test with a random parameter in the URL (e.g. ?test=1234) to force a non-cached load in Lighthouse.
• Compare with a test on the cached version and reduce the gap; aim for under 2.5 s even without cache.
• Optimize uncached load time so the cache is a bonus, not the only optimization.
• Configure the CDN to ignore irrelevant URL parameters (e.g. UTM, gclid) to preserve cache usage.
• Anticipate the upcoming No Vary Search standard, which will let you define parameters to ignore for caching.

Source: Search Engine Roundtable

The difference between the LCP metrics shown in GSC and CrUX is often a source of confusion. If you’re in this situation, Barry Pollard’s clarifications should help you see things more clearly!