Hello!
You're correct; there has been a significant back-end change, as the new PageSpeed Insights front-end web application as well as the new V5 API both are powered by Lighthouse (whereas previously they were independent tools).
As a result, the score changes you're seeing are reflective of Lighthouse scores (see more information on the
transition and how
Lighthouse scores performance).
Ultimately, you'll be able to increase your site's speed by following the guidance presented in the PSI report (see 'opportunities' section(s)).
Thank you!