Slightly embarrassed. I am still very new to SCCM.
No need, everyone is new at some point to all kinds of things.
First tip: It's not SCCM (for a variety of reasons). Many/some folks still refer to it as such, but it's really not and really never was. That's a whole side, semantic, ideological discussion/argument though that's more or less irrelevant.
The first log shows an error code of 53 when attempting to connect. Assuming the FQDN noted (since I can't see what it is and it wouldn't mean anything to me anyway) is for the "new" site system, that's the root cause here.
Error code 53 means "The network path was not found." This literally means the system is not accessible on the network (from the primary site server in this case) and is typically indicative of a name resolution (DNS) issue but could also be a firewall issue or the system simply not being online or powered off. There's no definitive way to know which it is without troubleshooting and possible direct examination of the system itself.
One question you missed answering was whether or not you used a new name for the new site system?