LTE Hat for Pi doesn't work after restart

I’ve recently bought the LTE Hat for the Raspberry Pi ( Clipper HAT Mini (LTE 4G for Raspberry Pi) ), but it doesn’t work correctly: After attaching it to the Pi and booting from a newly-flashed OS it works fine, but after restarting the Pi (by removing the power) it doesn’t respond anymore and no led is glowing.

I can reproduce it on my Pi (Zero 2 W) with the following steps:

  1. Flash SD Card
  2. Boot from SD Card
  3. LTE Hat is glowing
  4. Remove power
  5. Insert power again
  6. Wait for Pi to boot
  7. LTE Hat is not glowing (and it doesn’t respond in minicom)

Neither more restarts nor the reset script from Getting Started with Clipper HAT Mini help.
I’ve tried it on two different raspberry pies, but the problem is the exact same each time
How can I fix that?

(Duplicate, the fix from CLIPPER LTE Mini HAT does not start - #6 by alphanumeric works)