Hi dot2222,
Welcome to Apple Support Communities. We understand you're seeing, "Network Offline" in the Mail app of your iPhone.
Accessing your emails to complete your daily tasks is an important feature on your iPhone. We'll be happy to help.
Do you experience this behavior on both cellular data and Wi-Fi? We suggest to test on both cellular data and Wi-Fi to help determine if this issue is specific to a network connectivity In addition, are you able to browse the web without any issues on your iPhone? If so, we suggest to follow these helpful steps: If you can't receive email on your iPhone, iPad, or iPod touch
You mentioned having the latest version of the iOS software. Just to be sure, you'll want to verify that your iPhone is updated to iOS 14.0.1. Having the latest update helps provide software improvements on your device.
We look forward to hearing back from you with an update.
Best regards.