Day One Classic (version 1) has been retired since March 2016 and no longer is functional on iOS 15 or later. There are options to import Day One Classic data stored in iCloud to the new version of Day One.

iOS

Download the new Day One from the App Store and update to version 7.20 or later on the App Store.
Go to Day One > Settings > Import / Export and tap Import from Day One Classic. Screen shot below.
You will be prompted if you would like to import your journal. Tap Import. You’ll see a progress indicator.
After the import is complete, your newly imported data will appear in a new journal titled Journal. If you’ve imported a journal previously, or already have a journal titled Journal, your imported data may appear in a journal titled Journal followed by a number.

The new Day One supports one journal with the Basic account status. Journals can be managed in Settings > Journals.

macOS

Importing from File Menu

With both Day One Classic and the new Day One installed on the same Mac, please follow these steps:

Go to File > Import and click Classic app.
You will be prompted if you would like to import your journal. Click Import. You’ll see a progress bar.
After the import is complete, your newly imported data will appear in a journal titled Journal. If you’ve imported a journal previously, or already have a journal titled Journal, your imported data may appear in a journal titled Journal followed by a number.