Because you can connect to both IPs from the local network but not from the outside, it seems that the connection is blocked by a firewall (e.g. on a router / gateway). This will not occur when using VPN (the firewall let the VPN packets pass).
If your firewall provides logs, you may check them to see which packets has been dropped.
AFAIK WMI uses port 135 or 445 to make a connection and then chooses a random port for communication. While the local firewall knows this port number, a firewall on a gateway system does not. To avoid using random ports you can configure WMI to use a fixed port:
Setting Up a Fixed Port for WMI (Windows)[
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Then configure your gateway firewall to allow the required ports (TCP 135, 445, and the fixed port for WMI). But be aware that allowing incoming traffic on TCP ports 135 and 445 is dangerous (especially on a gateway system). So you should limit it to the public IP of your system to protect other systems in the local network. For security reasons it would be much better to use the local IP via VPN instead.