Thanks for your answer. Capacitors were indeed not needed and harmful. I removed them. The situation has improved, but just. E.g. ULN2003A is not scorching hot, just very hot. And of course once I raise the pwm duty cycle, it becomes barely warm.

@Andyaka: Fans draw around 0.2A each, and PWM frequency is 32kHz now. The capacitors were put there to reduce audible noise from fans, initially the PWM frequency was much lower.

Thanks for the screenshot and the explanation. Will try building something like this. In all fairness, though, @CMP posted this video link as a comment above earlier...