This appears to have been addressed as of Jan 2025 and our own testing does show success with mixed case Bundle IDs.

Apples docs seem to indicate that listening for changes on Activity.pushToStartToken updates is the place to handle an incoming push to start notification. That sequence does provide updated tokens, but nothing else. Instead, use Activity.activityUpdates, which gives you the information in the pushToStart notification payload (ie: actual attributes, contentState). This is also where you can download images and pass them to the appGroup.