I'm trying to share an internet connection from a host computer's wifi to another computer connected via ethernet while also allowing both computers to directly talk to each other over the wire. The goal is to have various programs work with each other quickly rather than rely on the wifi's connection as I often use them in tandem. I tried the internet connection settings but the host can only ping the other computer, not the other way around. A network bridge seems like the best option, but that doesn't seem to allow access to the internet over wifi even though Windows says I'm still connected to my router. I've also tried both setting the bridge's IP to that of the unbridged wifi connection, a unique IP, and DHCP but none allow internet. The computers also don't seem to talk to each other. All drivers appear to be up to date.
Is this kind of connection possible? Appreciate any help or troubleshooting tips!
Per request, here are a couple of diagrams.