Which app is safe to restore deleted emails and text messages?

There is no app, safe or otherwise, to 'get these items back'.

Check the trash in your email.

For messages, in the conversation list, tap on edit, and look at the recently deleted messages. (this assumes you're running iOS 16)

In addition to what KiltedTim correctly suggests (there is no App which you can find that can restore things you delete), if your email messages aren't in your deleted folder, you can contact your email provider who usually has a way to restore deleted email back to you as they will still be on their servers.

If a text message is deleted and it's not in your recently deleted folder, it's gone.

If a picture is deleted and it's not in your recently deleted folder, it too is gone.