Yes it’s entirely possible.
Many web proxies (most?) are HTTP proxies (also called level 7 proxies) and have two, separate, HTTP connections - one for the incoming “frontend” and the other for the outgoing “backend”. These two connections can have completely different settings - including supporting different HTTP versions.
Other proxies are TCP proxies (also called level 4 proxies) and they have no concept of HTTP and just forward the TCP packets on and assume the otherwise will know what to do with them. In this case it is not possible
To have different HTTP versions.
Saying that, most of the benefit of HTTP/2 is for the front end connection as HTTP/2 improves the performance impact of HTTP over high latency connections. Typically backend connections are over lower latency, higher bandwidth connections (maybe even in the same data centre). So while what you are asking is entirely possible whether you want to do this is more questionable. And it’s probably because of that questionable benefit that many servers don’t actually support backend connections over HTTP/2. Apache does but has it marked as experimental. Nginx does not and say they won’t. I’m not familiar with Go but looks like it might support this.