Proxy SwitchyOmega (and similar extensions like V2Ray Proxy SwitchyPro) doesn't contain V2Ray itself. Instead, it acts as a for Chrome. It tells Chrome which websites to send through your locally running V2Ray proxy and which to connect to directly.
A handful of developers have attempted pure V2Ray extensions. One notable example is (now largely deprecated). It attempted to implement a limited VMess client inside an extension. v2ray extension for chrome
: Avoid running a heavy background client if you only need privacy for web surfing. Quick Switching Proxy SwitchyOmega (and similar extensions like V2Ray Proxy
: Click the extension icon and select Options . v2ray extension for chrome