If you are their banking customer with a savings account or little higher variant of account or existing customer in form of loans or any other viable financing was done earlier, they could treat you better!
Your screenshot says 15 days, probably after this, You would have verification by some agent done and then you would receive your card perhaps utmost by 2 weeks
For me it took 3 weeks and the limit was so less. I believe it depends upon your location. But do expect a waiting time of 10 days to 3 weeks. They would send you an email with link to track the status
In my experience, i have noted axis bank do have some strict internal policies. But if it's approved then it should be dispatched. I would suggest you to visit axis bank branch to get clarity if it was actually approved or not. And If it's approved. Ask them what's the problem of getting it...
Lic - tech term plan,
Max life - smart secure plan,
Reliance Nippon,
Kotak Mahindra - e term plan.
Tata AIA - Sampoorn Raksha Supreme.
You can check on these for a starter then pin down based on your requirment.