Why is the past tense "got" used here when he's asking about the present situation?
He is not using grammatically correct English which is why he uses "got" here in a present tense situation. Instead, he should have said, "what do we have here?". It would be correct to use "got" in this situation if the main verb was "have" instead of "do" and if he had said, "what have we got here?". When "have" and "got" are together, they form the present perfect tense, even though "got" by itself is a past tense verb.