It seems what I've figured out what's gone wrong with new PCB
For the reason, I use transistor to cut off connection between coil and power supply, ground is connected permanently and control circuit tracks current on electromagnet to choose duty cycle properly.

That's why transistor works like common-drain-amplifier.
Drain current derives from difference between gate-voltage and drain-voltage multiplied by forward transconductance of a transistor, so drain voltage cannot be greater than gate voltage minus voltage drop on gate-drain junction, that's why you can see something like this:

Yellow - control voltage, from logic gates (5V amplitude)
Violet - drain voltage

Well, what's next? There is three options, actually:
- One option is to find a way how to use common-source-amplifier schematics there, but I'm kind of skeptical about it, because such a control method leaves many limitations
- Second option is to amplify control voltage to V_TRG level, by additional transistor, which works in common-source mode. This should work nicely
- Third option is to use solid-state relays, they are cool, but kind of expensive, so I don't think that this is an option for small and not-so-powerful actuators

P.S. You might wonder, why I made such a mistake. Well, everything worked well on a previous design! I have no idea why and how, because now I see that it shouldn't. However, it worked
Maybe it was some kind of magical interaction between Q1 and Q2, uhuhu : )