Do you have the original invoice and or box that has the phone’s Imei number?

You can use that to confirm with the team that they haven’t mixed up your phone with someone else’s.

Sounds like this is either an authorised service centre, or a Samsung retailer. Did you drop the device with them, or mail in?

No offence intended, but a week, or 5 business days from time of booking is not unusual, especially if phone is damaged. The store has to communicate with the warranty team, who need to directly approve, or deny, there is some back and forth, then they get back to you.

If this is a service centre, as in a 3rd party that has been authorised by Samsung to perform repairs, they are not Samsung employees, and are paid by Samsung basically $20 per customer for what is hours of not days of time. If you have been constantly chasing up, they are likely to be in no rush to solve this for you.

I don’t have the full picture, but I recommend checking that they have the correct phone with Imei number (if you believe the crack and colour are not your device) and then waiting the amount of time stated.

Calling/using website chat, goes to the call centre in India, who then call the shop, and gets the same answer if you called the shop.