Very weird indeed. I applied for Axis Airtel CC from Airtel Thanks app. It immediately gave me the option of video KYC. After clicking on that link, I was on hold on their mobile website for around 40 minutes (6 PPL ahead in q), but process was smooth. I had to answer basic questions and hold PAN card. After completion, 7 days later, card was approved. And I received it 2 days after approval.
After first transaction, joining fee of 500+GST was charged and 2 days further, I received 500 Amazon voucher in email.
Overall process was pretty smooth.
OP, where did you apply the CC? Axis website or Airtel app? Not sure if that makes a difference. Looks like you did not get a link for video kyc