Help to authenticate a bottle of Ombre Nomade LV (photos included)

Hello everyone, I have this bottle of Ombre Nomade from Louis Vuitton (batch code: 3C01, i.e. March 1, 2023), purchased second-hand. The bottle seems compliant (deep black glass, gold lettering, magnetic cap, clear engraving under the bottle), but I am surprised by its lightness and lack of staying power, which is unusual for this famously intense perfume.

Here are some photos for review. Do you think this is a genuine bottle or potentially re-filled/fake? Thank you for your feedback.