All contacts and apps did not transfer to new phone

If you followed these instructions everything will transfer—>Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support. Note that Music and apps do not “transfer”. They are automatically downloaded from the iTunes/App Store after the first step of the transfer has completed. You need to leave the phone connected after the initial data transfer to get back your music and apps.

Only iCloud contacts will transfer. Contacts from other sources (gmail, yahoo mail, microsoft mail, etc) are synced to the phone when you add the associated accounts in Settings/passwords & Accounts.

You can verify if all your old phone's contacts are on your iCloud Account here ---> iCloud.com