There is an item "Change text size" in "Screen display and brightness" of the setting app, and you can change the size of the characters displayed in the app by operating the slider there. The same operation can be performed using the "Text Size" button added to the Control Center.
If you change the size of characters in this way, the system will automatically handle adjustments such as line spacing, so the layout will not collapse even if the characters become large or small. However, it does not apply to all apps, and some apps have the same font size.
The reason is in "Dynamic Type". Dynamic Type is a mechanism to determine the character size (font size) that is common to iOS apps, and decides whether or not to support it when developing the app. In other words, the setting contents of the "Change text size" screen will not be reflected unless the app is developed to support Dynamic Type.
In terms of iOS standard equipment, applications such as "Mail", "Calendar", and "Contacts" support Dynamic Type. Since the iOS functions that are responsible for the overall display of the home screen also support Dynamic Type, the font size of the text of the application name and notification dialog will change depending on the setting of the "Change text size" screen.
On the other hand, the size of characters does not change for apps that are not developed to support Dynamic Type. This is because in the case of an application in which the display position of characters, etc. is fixed, such as games, inconvenience may occur if the display elements are enlarged or reduced. For third-party products distributed on the App Store, you should basically think of it as a function for apps that mainly read text such as e-book viewers.