My LB wakes up once during the night at around 3-4am and he gets his bottle of milk. I've tried different methods, he won't drink water during the night and if he doesn't get his milk he will be awake until 7am. So for the time being I just let him drink it in the middle of the night, it's not worth the fuss, he falls asleep immediately after drinking it.
I just let my boy have milk until he decided he didn't want it anymore, he now has it either morning or before bed and rarely finishes the bottle now he has it in a MAM toddler cup with a hard spout. He'll wean himself off eventually, if it helps him settle back off to sleep keep giving it I'd say, don't stress yourself.
Update - he did eventually go off to sleep after 4.5 hours! And slept 5.30am-8am which I will take as a small win!😂 I am tired!!