First, disable iCloud syncing selectively. On your iPhone, go to Settings > [Your Name] > iCloud. You'll see a list of apps and features that use iCloud. Toggle off everything - Photos, iCloud Drive, Messages, Contacts, Calendars, Reminders, Safari, and any others you’re not using. When prompted, choose “Delete from iPhone” if you're asked whether to keep the data locally. This will prevent your iPhone from continuing to sync any iCloud content without affecting what's already stored in iCloud.
Next, make sure iCloud Backup is turned off. Still under the iCloud settings, go to iCloud Backup and turn it off if it’s enabled. This prevents your device from trying to back up to iCloud, which can also trigger alerts and notifications. Additionally, it's a good idea to disable iCloud Keychain, which manages passwords and can also create syncing issues. Go to iCloud > Passwords and Keychain and turn it off there.
To address the red badge notifications you're seeing in Settings, check the banner at the top of the main Settings screen (under your name). These often relate to specific features like iCloud Drive, Messages, or Keychain trying to sync. Tap the banner and either disable the features it references or follow the prompts to resolve any pending issues. You can also tap into each individual iCloud feature under Settings and ensure it's fully turned off.
If you're looking to go even further, you might consider turning off Find My iPhone under Settings > [Your Name] > Find My > Find My iPhone. This is optional but worth considering if you're truly not using any iCloud services. Just be aware that disabling Find My reduces your ability to locate the phone if it's lost or stolen, and you’ll need to enter your Apple ID password to turn it off.
In summary, you can stay signed in to your Apple ID while completely disabling iCloud syncing. Going through each iCloud feature and turning them off individually will stop sync attempts and should eliminate the red alerts you're seeing. Your iPhone will continue to function normally, and you'll still be able to use the App Store, iMessage, FaceTime, and other Apple services that rely on your Apple ID.