Powering Raspberry Pi Zero W and LED-Strip with 24v DC
The PI Zero seems to take 120 mA max.

The PI Zero is not supplying power to the LED strips so you should be totally fine. If anything the TLE4271 is probably overkill for this task.

my only concern is that the 24v input power supply that came with the led strips has no margin for the extra 120mA for your PI. You should check the 24V power supply's current rating too.