Apple ID confirmation by Apple support - Privacy concern

Today I connected with Apple Support over chat because my Facetime and iMessage was not activating. So the person helping me out asked me to confirm a pop-up he had sent remotely which stated something like this : "Would you like to confirm your Apple ID and allow Apple to access the serial number of each of your devices to expedite your interaction? If you did no contact Apple, do not confirm this request."

So I went ahead and Confirmed. The issue was resolved and I could sign in to Facetime and iMessage.

I just wanted to know, if confirming the popup allows support or anyone to access my phone remotely and should I be worried about any security/privacy concerns? If anyone has a similar experience please let me know.

TIA.