Anecdotal reports basically, obviously 10x is just a round number I picked. I've seen a company that switched citing up to 40x hardware reduction going from Ruby on rails to Go.
I think you're significantly underestimating how well-performing PHP is, in the narrow but important field of serving dynamic web pages. Go (or Java, or C#) can be faster but you might be surprised that it's less of a slam-dunk win than one might expect. Python and Ruby basically aren't in the same league. Nodejs can be said to be licking at its heels, at best. Yes, seriously.
I'd put PHP somewhere under the middle of the list of languages/ecosystems I'd like to work in again (RoR, specifically, though not Ruby generally; non-TypeScript JavaScript; and gnarly AbstractFactoryImpl-style Java are all probably worse than it, IMO, and of course PHP deep in anything like Wordpress is pretty miserable) and I like Go quite a bit, but there's no denying that if performance is a top criterion PHP should probably be on your short list when choosing a language/ecosystem, and if PHP's not going to cut it then probably no scripting languages are on your list, and you're very likely looking real hard at C++.
I'm sure they would love to hear from you if you can cut 90% of their hardware costs without increasing other costs.