Hello danappl,
Welcome to Apple Support Communities!
We see you viewed the Apple Support page for Add verifiable COVID-19 vaccination information to Apple Wallet and Health - Apple Support
We want to help get your vaccination card added into your Wallet as you expect.
We want to confirm you're taking these steps:
"If you received a QR code
You can scan a QR code given to you by your COVID-19 vaccination or test provider to add your verifiable health records to the Health app.
- Open the Camera app from the Home Screen, Control Center, or Lock Screen on your iPhone or iPod touch.
- Select the rear-facing camera.
- Hold your device so that the QR code appears in the viewfinder in the Camera app. Your device recognizes the QR code and shows a Health app notification.
- Tap the Health app notification.
- For verifiable vaccination records, tap Add to Wallet & Health to add the record to the Health app and Wallet app.
- Tap Done.
If there's a change to your vaccination record, such as receiving an additional dose, you'll need to add a new QR code."
The Apple Support page you visited has those details: Add verifiable COVID-19 vaccination information to Apple Wallet and Health - Apple Support
Restart your device if you still the error after taking these steps and then try again.
If the issue continues, please also check for any pending iOS updates, which can help make sure the software is working as expected. This Apple Support page can help get those updates installed: Update your iPhone, iPad, or iPod touch - Apple Support
"Update your iPhone or iPad wirelessly
- Back up your device using iCloud or your computer.
- Plug your device into power and connect to the internet with Wi-Fi.
- Go to Settings > General, then tap Software Update.
- Choose the software update that you want to install. You can choose to stay on iOS or iPadOS 15 and still get important security updates. Or you can choose the option to upgrade to iOS or iPadOS 16.

5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do."
We hope this helps so you can get the card added into Wallet without any errors.
Cheers!