Google announced that its PageSpeed Insights tool as of March 3, 2021 uses http/2 to make network requests, that is if the server supports it. If your site is on HTPT/2, you may see your PageSpeed Insights scores go up as a result.
No, your rankings won’t go up as a result but just a heads up.
Here is the announcement:
As of March 3, 2021, PageSpeed Insights uses http/2 to make network requests, if the server supports it. Previously, all requests were made with http/1.1 due to constraints in connectivity infrastructure. With this improvement, you can expect more similarity between Lighthouse results from PSI and from Lighthouse CLI and DevTools (which have always made requests with h2). However, it’s important to keep in mind that different environments (hardware & connectivity) will influence measurement, so cross-environment consistency is near impossible.
With this change, network connections are often established quicker. Given your requests are served in h2, you can likely expect metrics and the performance score to improve. In general, performance scores across all PageSpeed Insights runs went up by a few points.
If your page does not support h2, the report will now show an audit that estimates the performance improvement if the page were to support h2.
Note, GoogleBot supports crawling sites over HTTP/2 as well.
Forum discussion at Twitter.