How do I play the correct turret animation based on player direction?

Do you want to keep the turret rotation active?

If you want to keep the rotation handled by the turret then you will need to change all the Animation frame Angle to face (angle = 0)

So they all face the same direction, otherwise, it will conflict with the turret rotation.

Then one idea you could do is to keep the events short and clean:

Change the Animation names to:

R = 0

L = 180

Up = 270

Down = 90

Then you set the turret Animation to:

str(round(((angle(Self.X, Self.Y, Player.X,Player.Y) + 360) % 360)/90) * 90)

You can also use the every x seconds to change the animations, maybe something small Every 0.3 or something like that.