Check for Jailbreaks
In order to install spyware on an iOS device, attackers need to exploit vulnerabilities in the operating system. Apple has made this task significantly harder over the years, and such exploits have become more difficult and more expensive to produce. Remote Exploits (attacking, for example, WhatsApp, iMessage or Safari) are particularly rare and costly, and are only accessible to resourceful attackers, typically governments. In the case that an iOS device was indeed compromised with a private, commercial-grade sophisticated exploit, it is likely the case that the only check you can perform is of the outgoing network traffic.
Jailbreaks are exploits for mobile devices, in this case iPhones and iPads, that are typically installed manually on the phone and which disable certain security features of iOS. New jailbreaks are regularly made available to the public and attackers might use them if the target devices are of the right model and version of iOS. At the time of writing, there are public jailbreaks available for iOS up to version 12.2.
Because regular users typically would not (and should not) install jailbreaks on their iPhones and iPads, if the device you are testing shows appears jailbroken it is a very credible sign of a potential compromise. Following are some of the traces that might be left behind by a public jailbreak.