Is there any benefit for having multiple copy of a same luxury resource?

According to what I can find in several online Civ VI wikis, your testing is correct. A luxury resource type provides it's benefit once, and additional copies do not increase this, but I will check the official sources for confirmation.

While the in-game Civilopedia does not explicitly spell it out, it does seem to agree:

"Each type of Luxury resource can contribute up to 4 Amenities to your empire (1 per city) to the 4 cities that need them most."

But it is explicitly stated on page 50 of the Civ VI manual:

"Only one source of a specific luxury provides amenities, shared with the four neediest cities in your empire. For example, if you have 2 Citrus resources improved around your capital, only the first will be providing amenities to your empire. You can choose to trade the second Citrus with another civilization for something else you need, like Gold, or another resource."

https://downloads.2kgames.com/civilization/vi/manuals/eu/CIV_VI_25TH_ONLINE_MANUAL_AUS.pdf

Seldom-seen edge case: the World Congress might bring up the question of tweaking a luxury resource. Civs vote on which resource to tweak, and if it should provide zero amenities, or instead if multiples per civ should provide extra amenities. So for those 30 turns, you might be able to make use of two citrus to provide an amenity to 8 cities.