It could be just a greeting, but days of the week have significance for working people. "Happy Friday!" might be said more joyfully, sincerely, and commonly than "Happy Monday!", which might be said with a grumble as a joke.

It as simple as wishing for someone to have a good day. The speaker is wishing for the listener to be happy on whatever day of the week is specified.

It is a way of saying "good day" or have a good day (effectually, a way of well-wishing), on a specific day, but nobody says "happy Monday" or in reference of any one of the days of the week.

You can say "Happy birthday" or "happy holidays" or "happy [specific event]", but not "happy Tuesday" for example.

Just say "good morning/afternoon/evening", both as greeting and farewell.

You can also say "good day" as an adieu.