How can you tell if someone has put an app on your iPhone

Here is some Apple-provided security-related reading.

Parts here may or may not apply to your specific case...

Checklist: If you want to stop sharing with someone whom you previously shared with - Apple Support

Checklist: If you want to make sure no one else can see your location - Apple Support

Checklist: If you want to see if anyone else has access to your device or accounts - Apple Support

Device and Data Access when Personal Safety is At Risk

Robust and unique passwords are a key part of maintaining security, as are reliable and complete backups.

To put an app on the phone requires physical possession of the phone while it was unlocked. Did you give the phone to someone who might have done this?

And even if an app was installed on the phone it would not be able to record anything you do on the phone, let alone everything, unless the phone was also jailbroken, which again requires physical possession of the phone while it is unlocked.

Also, SyllableX is correct, and even in that case they can’t see everything, only a few basic functions such as location and email.

Unless your phone is managed by an administration such as a business or school, it's not possible for an app to see everything you do on your iphone