I actually tried using Proxifier to attempt to make this functionality work, both by adding an Orion web app (i.e., an SSB) into Proxifier, as well as an Orion profile app, and even the main Orion app itselfโyet sadly, none of my efforts panned out.
It seems that Orion utterly refuses to proxy the actual, rendered browser content through any kind of proxying mechanism, whether via a Chrome / Firefox extension (like the ones that have already been mentioned previously on this thread), or even something that operates at a lower system level, as Proxifier does.
For reference, Proxifier normally works with any native app, e.g., Mail, Messenger, etc. Although I have noticed that Proxifier has some odd behavior with Safari, in that some websites appear to funnel through the proxy, while others do not.
Still, the fact that Proxifier doesn't work at all with Orion is very peculiar and unexpected. I'm guessing Orion must be doing some rather fancy WebKit-based tricks which prevent traffic from actually going through a singular binary file, as opposed to a normal macOS app.
As with everyone else on this thread, I would like to echo that this functionality should either become a part of the browser itself as soon as possible, or efforts should be made to accommodate the usage of browser extensions like Proxy SwitchyOmega, Proxy SwitchyOmega 3 (ZeroOmega), FoxyProxy, etc. (I tried all of these, and none work in Orion).
Attempting to force a proxy via system-level tools like Proxifier shouldn't be necessary to enable this crucial functionality in Orion, although the fact that even Proxifier doesn't help to alleviate this issue underscores the need for developer attention on this.
As with others above, I rely on SOCKS proxies for work and cannot use Orion as my daily driver unless support for this feature is added. This is a real shame, as I was intending to try migrating to it as my main browser, until I found out about this very frustrating problem.