I had a genious thought. These Li-ion protection boards are about 0.14 euro,

while there are also these 0.17 euro TP4056 1A Li-ion chargers including the protection circuit, which I had still lying around.

So I quickly hooked it up and tested it 

And it works well. Then I designed a new PCB and ordered from JLCPCB and soldered it.

Now I feel happy