OP your breast pump is not a nebuliser, it's not medical equipment in any shape or form.
You dh has a long commute. So I assume he is in bed before 11pm.
Being woken up at 11pm and 3am for 15 minutes a time (he doesn't even have to be fully awake just take his ear plugs out) isn't going to exhaust him. If it does he can go to bed earlier.
Your baby is yours and dhs. Neither of you can expect your dh to have a full nights sleep every night. Especially when you are working so hard to maintain supply.
The baby is not your neighbours. It's not ok to take steps that disturb her but not your dh.
Maybe your alarm is waking her up, but not fully, then the vibration is just enough to keep her awake.
She obviously can hear it (can't understand why people are questioning whether she can) because she commented. If she was sleeping through, she wouldn't be asking what the mechanical noise was.
What do you when the baby sleeps during the day? Sit by the baby?
Do you go to bed I am evening when the baby does.
Your baby does not need the mother in the room to regulate breathing.
Studies show being hear a parent may help regulate breathing. Your husband is also a parent.
You are making life incredibly difficult for yourself. Your DH needs to help out.