Since web proxy was originally used near clients, caching stuff to save precious bandwidth of their kbps-tier connection.

It's one of the classic cases of a thing being named relative to what came before it, rather than being named on its own merit. This makes sense to people working at the time the new thing is introduced, but is confusing to every other learner in the future.

Nowadays, "reverse" is suppressed in most ways. I have heard that Nginx is a proxy more often than a reverse proxy.