To clarify things a bit:
The client on the relay is trying to connect to 127.0.0.1, which is the loopback address. If a relay service is running on the same computer as a client the client will always try to use the relay running on the same computer via the loopback address. It will do this no matter what relay selection method you have told the client to use.
If you need to reconnect to the client, you can stop the relay service and then the client will revert to normal relay selection and find another relay. You may need to restart the BES Client service as well, if just to speed things up. This can be useful if you want to try uninstalling/re-installing the relay via fixlets.
Basically the “client on the relay is not registering with a relay” issue is not a network issue. Now the fact that the relay is also not reporting in (if I am reading your first post correctly) would point to the fact that it’s the relay that is the issue.
Could be TLS 1.2 is not enabled on the relay (I have seen this cause very similar issues) so it can’t communicate with clients, other relays, or root. Could be something else wrong with the relay configuration. I would probably start by double checking that TLS 1.2 is enabled on the relay server. If it is, then I would try running the BES Remove Utility to completely remove the relay, restart the BES Client service, wait for the client to reconnect to another relay, then re-install the relay via fixlet.