If you want to turn off Private Relay notifications without disabling iCloud Private Relay itself, there is no separate setting available to do so.
These notifications are system-generated alerts intended to inform you when iCloud Private Relay is unable to function as expected on a particular network. Private Relay is a privacy feature of iCloud+ that helps protect your privacy by concealing your IP address and limiting the ability of network providers and websites to associate your browsing activity with your identity.
If you connect to a network that is incompatible with Private Relay, or if the network administrator or carrier restricts its operation, your iPhone may display a notification indicating that Private Relay is unavailable or has been turned off for that network. This is to make you aware that your browsing privacy may not be protected by Private Relay under those circumstances.
These notifications do not, in any way, stop your browsing activity or prevent you from using your iPhone or other device. You can continue to browse the internet, use Safari, access websites, and use your device as usual. It is simply a warning message informing you that Private Relay's privacy protection is unavailable on the current network. Your internet connection is not necessarily interrupted.
These notifications serve an important purpose: they alert you when the privacy protection you have enabled is not functioning as intended. Apple does not provide a dedicated option to suppress these notifications while keeping Private Relay enabled.
Furthermore, these notifications are generally not persistent. They appear briefly on the screen and disappear automatically after a short period. They do not remain permanently displayed or interfere with your normal use of the device. They are simply temporary alerts to keep you informed about the status of Private Relay.
In other words, you cannot selectively disable these system notifications while retaining the feature in its entirety.