Learn English – nything like I shouldn’t say “Good afternoon” in corporate world but instead should use Good Morning and Good Evening only

Good evening. Good night is definitely for good-bye's only, not as a greeting.

As to whether you'd use "today" or "tonight", that might be a convention of that profession, or that particular set of people, so I don't think anyone can give you a single good answer for that.

I think the weirdness comes from the fact that this is not really a conversation, in the sense that it is not an exchange of information between people who intend to be talking to each other.

In some cultures (including the US, where I am), it is considered friendly to acknowledge someone entering (and leaving) your store with some kind of greeting. Asking after their health or well-being is a formula; practically no one expects you to answer the question in its actual meaning.

This is part of a set of formulas that I think practically every culture has for conversation in one way or another. There are papers written on the subject. In this case, perhaps you could think of it as the speaker's way of letting you know that they have noticed you and are free to talk with you; you can reply with any formula of your own ("fine", "ok", "better than a sharp stick in the eye") to acknowledge that they have spoken; if what you say sounds enough like a formula itself (the first two, not the last), then you will not be expected to continue a conversation.

But if you came into the shop looking for something you wanted help with, the fact that they said something might help you know they were free to listen to what you wanted at that time, in case you would otherwise have been shy about asking.