I know this is old topic, but I couldn't find any answers regarding this issue when searching over the internet. Only numerous request for fix, which none was answered.

I couldn't find what is actually causing this?
Is this graphic card drivers issue, where they eventually removed support for some "game specific" shader instructions that calculated correct shadows from texture transparency, or they simply never implemented/purposely removed the instructions for correct shadows rendering, because it was too demanding on hardware back then in 2014?

What seems odd to me is that I couldn't find any mentions of this quite visible graphical issue from around the time of XIII-2 Steam release, only from several years after.
That's why I'm not sure if the game was released like this or certain graphical drivers update later removed support for this.

It wouldn't be first game that used specific instructions for rendering, that was not used anywhere else, thus the support was dropped over time.

Also wonder if anyone still cares about this.
I mean, it's not game breaking. The PC port have much worse issues, but once you resolve those, this graphical issue is making the game experience worse, because it's quite visible on many occasions.

It's not just palm trees on the New Bodhum.
It's every single model that use textures with alpha channel transparency.

Not that it matters much after about half-year since OP's question, but shouldn't the correct link be
https://mega.nz/file/q9pjSSDI#K4wFR0XtAY4ql9DrpD1kTMieZU9vnf1ib_Ja_aQfmLE
since OP asked in FFXIII section?
Link posted by Scarlet Crusade is for FFXIII-2