I think I've messed up with this one.
See that LOAD on the schematic? It's STM32 with bunch of other ICs like opamps, LDOs, step-ups.
The problem is that during the "off" state current somehow finds the way through STM32 GPIO outputs (ESD diodes, etc.) to the gate of N-Channel MOSFET. And it occurs only when battery is closer to discharged state, doesn't make sense to me why there is no leak when battery is fully charged though. It should be noted that the prototype PCB has an additional resistor to ground on the GATE pin (tried 1k, 10k, 100k), but it seems that the gate voltage remains the same(

) - leak looks like a voltage source

. Currently, in "off" state, I can measure some voltage around 1.2v on 3.3v lines. Device looks disconnected and LEDs are not blinking.
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So, the only way is to switch to P-Channel high-side switch configuration?
I thought about adding diodes on GPIO lines, or maybe there is another solution.