I would say the bullet points at the top are not strictly correct. The response does not necessarily transit the proxy. Responses can be returned directly to the client (DSR).
Layer 4 proxies are a very specific sometimes food that most people should actively avoid until they need it because of the tradeoffs.
DSR is layer 4, and not in scope of this post.
https://blog.envoyproxy.io/introduction-to-modern-network-lo...
Layer 4 to 7 is useful in this case, as layer 4 involves forging tcp/udp packets, which is vastly different than say a http level reverse proxy.
There's a separate term for the bits of the OSI model that are actually relevant; it's called the IETF model.