They exist but seem to be only to OEMs and in Asia. I have been waiting for one of these forever. You may do better making an ITX build and adding in a card.
I don’t think it exists with 4 LAN ports and a Ryzen embedded CPU. The only thing closer to it that I know of are the DFI boards. They sell some with Intel CPUs and 4 LAN ports.
Hmm, this depends on your needs, but two NICs + WLAN is plenty for most people.
My recommendation: Buy a 10 Gb switch, and use a two-port Ryzen NUC-alike as firewall. In all likelyhood your connection to the internet will be lower than 1Gb, which means you will not be losing anything at all by going with a 2-port + switch solution.
Since 4 ports are such a niche usecase, make use of what you have available instead. If a 4 port NIC is a must, however, why not get a small form factor ITX case and a 4 switch Low Profile ethernet card.
Another popular option is the HP T620 Plus, which uses a faster version of the same CPU. The “Plus” version is one of the few thin clients to have a PCIe slot. Add an Intel based NIC and you’re all set.
You can find them used on eBay, often with a four port Intel NIC already installed. They’re typically configured with 4GB of RAM and 16GB M.2 SATA SSD. They max out at 16GB of RAM.
You can find an article and a couple of discussion threads about using them as a router over at Serve The Home.