Hi Az2423,
Thank you for using the Apple Support Communities! I understand you are unable to successfully update your Apple ID photo under Settings, and I'd like to help.
It sounds like you were able to get the Apple ID photo to update in Settings only after updating your vCard in Contacts. You should certainly be able to update your photo from Settings as well. Let's try this again. Navigate to Settings > [your name]. Tap Edit on the current photo, and choose a different photo to set up. Once completed, I would like you to force quit Settings by following these steps: How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support. Then, open Settings back up and see if the change of photo appears.
If it still does not show the new photo, please let me know if you also use 'Share Name and Photo' under Settings > Messages: Use Messages on your iPhone, iPad, or iPod touch - Apple Support. I ask because the photo set up here, can also be connected to the photo you see under your name in Settings.
Best regards.