What will you tell your 3 year old when you leave your baby, her sibling, to cry until he potentially vomits, goes purple and then passes out once he realises no one’s coming?
You wouldn’t let her cry herself to sleep and ignore her, why would you do it to him?
He’s still so little. He’s not waking to annoy you. He’s doing what babies do and he’s used to you responding to his needs, during the day and at night.
Letting him cry till he gives up isn’t a good message to him or your DD that you’re there for them when they need you. He can’t tell you how he feels except for to cry.
3 months is a long time in infant development, 2 months is as well. You’ve got time to see if he starts doing longer stretches. You can carry on cosleeping once he’s awake, at least you’ll be resting and dozing with him. You can practise with different types of dummies to see if that helps settle him without a boob. You can look into ways to get him settle without a nipple or a dummy.
I know you’re exhausted, most of us have been there. But you’ve parented in a way that’s in tune with him so far, meeting his needs, you don’t have to switch from that approach to literally leaving him to scream himself asleep in desperation and exhaustion.
You wouldn’t let your husband sob himself to sleep without trying to comfort him. Or your daughter. You wouldn’t leave an elderly relative sobbing in distress at night and not go up them even if it was exhausting doing what they need from you.
It’s only ever non verbal babies people justify leaving to cry themselves to sleep and they literally have no option as they can’t comfort themselves or express themselves in any other way.
Please look at other gentler options.