Eventually, my mechanic directed me over the phone how to resolve this.
There's a small electric motor above the right front wheel. This motor is a part of the tilt-lock mechanism. It has a small black rubber cap that you need to remove, revealing a little valve you can turn with a slim flat-head screwdriver.
Just turn that valve a little to the left and to the right, turn the scooter off and on again, and try to release the tilt-lock again (you can put the scooter on the rear stand so that it doesn't fall when the tilt-lock releases).
If it doesn't release with your weight on the seat, try tapping the release button twice fast.
This worked for me just now, and now it's working fine.
1. Front view
2. Closer look
3. Black rubber cap
4. Valve (you can see the little place for the screwdriver to turn it)