You can't send an image for example from Claude iOS app to remote control session. With this new channels the attachment you send from Telegram bot is saved into your local Telegram inbox folder ready for you to process.
I believe its similar to PayNow Singapore, UPI India, PromptPay Thailand etc where you register your phone number with your bank app, you can send money to those mobile who are on the same network using your bank app, or use your bank's app to scan a QR when making payment to a vendor. The QR code is actually the vendor's number. There are now cross border link, for example I can send money to someone in India using just his mobile number on UPI.
I imagine in a few years our phone will become our AI assistant, locally and cloud powered, that understand us deeply. And Apple will release a human robot, loaded with the same intelligence in the phone to become our home assistant or companion. But first Apple needs to allow us to rename our phone agent/helper other than Siri.