A solid overview of the impact that Core Web Vitals, PageSpeed, Lighthouse, and other metrics actually play in terms of a website's Google Page Rank.
On the actual relevance of Lighthouse scores (not as much as you'd think):
Google takes URL-level Core Web Vitals data from CrUX into account when deciding where to rank you in a search results page. They do not use Lighthouse or PageSpeed Insights scores.
On the aspects that Google does care about:
To get a ranking boost, you need to pass all relevant Core Web Vitals and everything else in the Page Experience report.
This means your rankings are reliant on your performance in Chrome, even if the majority of your customers are in non-Chrome browsers.
On why Google searches on mobile often return different results to desktop:
This means that your placement on each device type is based on your performance on each device type.
On the impact of SPA architecture (yes, it is still an issue):
If you’re a Single-Page Application (SPA), you’re out of luck. While Google have made adjustments to not overly penalise you, your SPA is never really going to make much of a positive impact where Core Web Vitals are concerned.
Therefore, optimise every SPA page for a first-time visitor.