UPS based on TP4056/DW01/8205A not working - wrong components?

I built a small UPS according to this power backup circuit. I want to power my PiZero W with it. I soldered the components (see picture), A1/Si2301 pMosfet, 10k resistor, and B2 Schottky diode.


Unfortunately, it looks like the circuit does not work. I tested the following:

  1. Only connect battery to B+/B-, the output on the green PCB (+/-) equals the battery (4.2V).
  2. Only connect USB charger, the output on the green PCB (+/-) equals charger (5.05). The right LED on the blue PCB is on (blue), the left LED (red) is blinking. AFAIK this means that no LiIon is connected.
  3. I connect the battery to B+/B-, the output on the green PCB (+/-) equals the battery (4.2V). Then I connect the USB charger but the output is fluctuating around 4.10-4.20. No LED on the blue PCB is active.

I wonder if I made a mistake while soldering or if I used the wrong components.

Any idea why it does not work?
Thanks