If the camera is connected to the HomeBase, it won’t work with a NAS. Eufy doesn’t expose RTSP or direct streams from cameras routed through the HomeBase. That’s why your NAS can’t discover it.
For NAS support, the camera needs to connect directly to Wi-Fi, not through a HomeBase. Camerasd that support RTSP and can stream to a NAS require that option is enabled in the settings.
Eufy Link: eufy Support
Giving the HomeBase a static IP is a good step for other integrations, but it won’t help in this case.