@, I got it working in a very roundabout way. I connected an empty SSD to one of the PSU's power cables, and now the system works. But now when I shut down my laptop, the PSU stays on until I turn it off or I disconnect the TB cable. Weird. It would be still nice to know if anyone has any guesses about what's happening here.
Asus Expertbook B1500CEAE, Win11, 16GB DDR4, i5-1135G7, Iris Xe, R43SG-TB3, AMD R9 380, Corsair VX550W