…And saw another post here about this and wanted to confirm that I am experiencing the same thing.
Viewing the Conan Exile server listing on a PS4 Pro frequently (more often than not) brings the Internet connection down causing me to have to reboot the cable modem and router.
We use Charter. Conan Exiles on the PS4 is the only software/device in the house that actually brings down the Internet connection.
Could you temporarily try to turn off or disconnect any other devices that make use of the router, both wired and wireless, so that only the console is connected to it through cable?
Are you able to verify if your router provides logs to give further insight on the crash/error?
Could you also try using a different cable and/or switching the ethernet port that your console is using on the router?
Lastly, if possible, try to get a full router replacement, including its power supply (source).