It’s not a mistake actually it kind of indicates the problem may be the battery ground is disconnected from the circuit ground, which is what the battery protection circuit does.
Try doing a continuity test from battery ground to the usb ground, try doing it both polarities (flip the + and - probes). If you can also test the resistance, both polarities.
You can also do this same test between pins 2/3 and 6/7
I think you will find that if you “disable discharge protection” this should give continuity to this signal. You may not have it otherwise.
Can you take a good high res picture of all these components and we can inspect for any bad solder joints? Sometimes the jellybean parts go bad so it could just be the battery protection chip. That would explain why it turns on with the pins shorted it turns on… but not why it wouldn’t charge.