(This is a huge oversimplification of how things can work)
The email app is just acting as a container and pulling the emails down from whatever provider you’re with and saving them on your phone. So when you say “Safe” what exactly do you mean? Safe from who? Because really anything saved to your phone is only as safe as you make your device (Have a password to unlock the device)
If you’re talking about the safety of your emails themselves, it really comes down to your provider not which app you use. As if you use something like Gmail your emails are already being scanned on the regular regardless of what app you use on your phone. In which case you’re better to move to something like proton mail or tutanota.
tldr;
To quantify something as “safe” or not you have to ask yourself some more questions first and figure out your threat model.