If you have a 1SE Pro subscription, restore from 1SE Cloud instead: see How to Restore from a 1SE Backup. Otherwise, these steps move 1SE to your new iPhone with an iCloud backup.
Step 1: Back up your old iPhone with iCloud
On your old iPhone, follow How to Back Up with iCloud and wait for the backup to finish—the date under Back Up Now should be from just now.
Signing in to iCloud on your new iPhone is not the same as restoring from an iCloud backup. 1SE is not stored in iCloud Drive, so you need a full iCloud backup to transfer your data.
Step 2: Restore from an iCloud backup
Turn on your new iPhone. If it's already set up, erase it first: Settings > General > Transfer or Reset iPhone > Erase All Content and Settings.
Follow the setup steps until you reach the Apps & Data screen.
Select Restore from iCloud Backup and sign in with your Apple ID.
Choose the most recent backup that includes 1SE and wait for the process to complete.
When the restore finishes, open 1SE and your projects are there. If 1SE opens empty, the backup didn't include 1SE—go back to Step 1 on the old iPhone.
For more details, follow Apple’s guide on restoring from iCloud backup.
With a Pro subscription, 1SE Cloud Backup makes future moves easier.