iPhone did not transfer all existing content to new phone?

Apps don't transfer from iPhone to iPhone, only the app data along with app links to the App Store gets transferred.

After the transfer is complete (Quick Transfer, iCloud, or iTunes) depending on the internet speed all apps will get downloaded from the App Store automatically. If an App does not exist anymore in the App Store or the iOS version is not compatible with the App then the App data that is transferred cannot be accessed any further.

Apps & Settings --> Apart from the Apps following will also not get transferred between devices

1. Content from the iTunes and App Stores or PDFs downloaded directly to Apple Books
2. Content synced from iTunes, like imported MP3s or CDs, videos, books, and photos
3. Data already stored in iCloud, like iCloud Photos, iMessages, and text (SMS) and multimedia (MMS) messages
4. Data that are synced to an email account such as Google, iCloud, AOL, Exchange, Outlook, Yahoo, or any Other email client server that supports contact synchronization. e.g. Contacts, Reminders, Notes, Calendars
5. Face ID or Touch ID settings
6. Apple Pay information and settings
7. Apple Mail data
8. Apple Music