Google's John Mueller said on the last Google office hours that using HTTP/3 for your server will likely not have any impact on your SEO or rankings in Google Search.
He said it also would not likely lead to much or any gains in terms of your core web vitals scores.
John said "Google doesn't use HTTP/3 as a factor in ranking at the moment," and reconfirmed Google still does not use HTTP/3 for crawling.
John said this at the 6 minute mark in this video:
Here is the transcript:
Flavio asks, could the use of HTTP/3, even indirectly, improve SEO, perhaps because it improves performance?Google doesn't use HTTP/3 as a factor in ranking at the moment. As far as I know, we don't use it in crawling either.
In terms of performance, I suspect the gains users see from using HTTP/3 would not be enough to significantly affect the core web vitals, which are the metrics that we use in the page experience ranking factor.
While making a faster server is always a good idea. I doubt you'd see a direct connection with SEO only from using HTTP/3. Similar to how you'd be hard pressed to finding a direct connection to using a faster kind of RAM in your servers.
Forum discussion at Twitter.