Hi there,
Sorry for the confusion. If you're connected to Wi-Fi and otherwise have internet access, you don't need to troubleshoot your network because of this message.
Premiere Rush's Creative Cloud project syncing was discontinued, but Rush can still display this misleading “No network connection” warning. Projects stored locally on your device can still be opened and edited.
More information:
https://helpx.adobe.com/premiere-rush/desktop/kb/creative-cloud-files-end-of-life-for-premiere-rush.html
Sorry for the confusing message.
Thanks,
Kevin