iPhone Replacement Phone & Apple Repair Centre (Bangalore)

I bought a new iPhone 13Pro, 512GB, phone on the 24th of September (launch date). And, I had issues with my Face ID not working within 5 days of purchasing my phone. 

I took my phone to the Apple Service Centre in New Delhi (Defence Colony) and they ran tests which confirmed that my Face ID is not working, so they sent my phone to the Apple testing centre in Bangalore.

I was told on the 1st of October that they've confirmed that it will be replaced but gave no date of when I'll get my phone back. I've been following up with the Apple Centre in Delhi ever since, as they have no email address nor a phone number to give me of the Centre in Bangalore for direct communication, and all I get in response is that I'll take take another day or maximum of two days for me to get my phone.

It's the 9th of October today and their latest update for me is, that "the Bangalore Centre has asked you to please wait until Thursday or Friday of next week for an update."

I've spoken to and raised my concerns with Apple Support a few times, but they've been of no help. All they've asked me to do is to speak with the Apple Centre in Delhi to get updates since they should have more information, and said that they've taken my feedback.

I'm not quite sure if anyone has any advice on how to deal with this issue, but all I could think of was to put this up here and post how terrible Apple has been on other social media.

PS: I asked for a refund, so I can buy a new phone after instead of waiting forever, but they said that a refund can only take place within the first two days of purchasing the phone.