Google announced that starting in November 2020 it may begin to crawl some sites over HTTP/2. Google wrote "today we're announcing that starting mid November 2020, Googlebot will support crawling over HTTP/2 for select sites."
Google said sites that support HTTP/2 should see efficiency improvements with this change. Google said it "expects this change to make crawling more efficient in terms of server resource usage." Why? In short, it requires opening less TCP connections; Google said "Googlebot is able to open a single TCP connection to the server and efficiently transfer multiple files over it in parallel, instead of requiring multiple connections. The fewer connections open, the fewer resources the server and Googlebot have to spend on crawling."
This will start with a small number of sites in November and Google will then ramp it up as it sees how it goes. Googlebot decides which site to crawl over h2 based on whether the site supports HTTP/2, and whether the site and GoogleBot would benefit from crawling over HTTP/2, Google said. If your server supports HTTP/2 and Googlebot already crawls a lot from your site, you may be already eligible for the connection upgrade, and you don't have to do anything.
Google has a larger article with FAQs on this over here.
Just an FYI - Google said in 2015 this support was coming soon. But I think that was more on if GoogleBot can handle HTTP/2 sites in general, not that GoogleBot itself will crawl using HTTP/2.
And no, "is there any ranking benefit for a site in being crawled over h2? No." Google actually also said that in 2016.
Here is a bit more from Gary:
Super excited about this one! So much work went into this launch and so much careful evaluation! https://t.co/Mj7jCk5c43
— Gary 鯨理/경리 Illyes (@methode) September 17, 2020
Forum discussion at Twitter.