iPhone Locked: Unable to sign in to the App Store despite iCloud working

For a direct answer you will need to provide more information on exactly what you are seeing and a screenshot is always helpful as long as it does not reveal any personal information. The general Support Article for a Locked, Disabled, or inactive Apple Account is here:

If your Apple Account is locked, not active, or disabled - Apple Support

If you are able to open the phone to access Safari and the App Store, then it has nothing to do with the Activation Lock information that was previously provided. When it is an Activation Lock, the only thing you will see on the phone is a screen that says "Locked to Owner" and you will not be able to proceed passed that screen to open any apps at all.

Thank you for reaching out. 🤗

If you are not the original owner, then Activation Lock is a security feature to protect the owner from theft. In that case, only the original owner can unlock it. 🔓

↓ If you are the original owner: ↓

According to Apple:

Remove Activation Lock on the device

Follow the onscreen steps to enter the Apple Account and password you used to set up your device or your device passcode. If you don't remember your Apple Account, try to sign in with an email address or phone number that you regularly use for Apple services.

Learn how to find your Apple Account or reset your Apple Account password.

If your device is owned by a business or educational institution, please contact your IT department or manager. 

Remove Activation Lock on the web if a device is offline

For iPhone, you might be able to remove Activation Lock on the web even if your device isn't offline.

1. Go to www.iCloud.com/find.
2. Sign in to your Apple Account.
3. Select the device that you want to remove from iCloud.
4. Click Remove This Device.

Start a support request

If you need help removing Activation Lock and have proof of purchase documentation, you can start an Activation Lock support request.

Thanks again for reaching out. 👍🏼

Smiliñ 😎 Brian