How are their customers able to pay in Bitcoin? Is there a local wallet app in the country that is popular that could be used for the grocery transactions between customers and the store? I am asking because if transactions are all done on-chain, I might end up paying a bigger amount for fees than the groceries I'm buying. I might end up paying more for my transaction to be confirmed than the packs of coffee I'm buying. Or are they possibly making use of lightning network?
The supermarket is using Bitpay, you can pay with any wallet you want.
I'm not sure if Bitpay accepts lightning, but note that you can always order online, so waiting time for on-chain shouldn't be a problem:

In any case, fees are very low on-chain, for example
this recent transaction for about $600 just paid 21 cents in feesAlso, their clients paying with Bitcoin are getting 20% off until end of the year, that's a great discount.