Breastfeeding 3am

So my breastfed 3 month old cluster feeds at night I don’t mind this as normally I go to sleep while they’re feeding however recently they’ve been waking up at 3am and not going back to sleep for an hour or 2. I’ve tried everything, boobs, rocking etc I think by this time the baby has had all my milk so my boobs hasn’t refilled yet any tips to help this? We don’t have trouble during the day and normally no trouble in the night until recently. Last night I made a bottle out of the frozen milk I have in the freezer incase my mom has him for the day and he settled and went back to sleep so I’m assuming it’s because he’s not getting enough milk from 3am till about 4/5. I also think this because when I squeezed my nipple last night to see if he was getting any not much / hardly anything came out. I think he’s draining them and then waking for more.

During the day he’ll have a breakfast formula bottle and one about 2pm other than that he is strictly breastfed so I don’t pump before bed because I know he’s going to wake for it.

Tips please!