Sometimes your gut feelings are right. Be on the lookout for more red flags, they're sure to pop up. The thing is, unless you are indispensable to the company, they're possibly gonna axe you without a second thought. Your gut feeling is telling you there's a good chance of that. They company isn't going to care about your baby, it cares only about money. Even on the more personal level, your direct boss doesn't give a damn about you it seems, so don't count on human empathy to give you any leeway here.

The reality is you can't do much. It's not up to you whether you can save your position, if the company is planning to axe you then it's gonna do it without any regard to what you think is fair. So just keep that in mind, and plan your current situation to your advantage:

First I would check to see if they pay out PTO. Some PTO like floating holidays or personal days may not get paid out (read your contract). Optimize on taking that PTO first, immediately. Since you have a baby, take your parental leave soon. Even if they lay you off, you can get severance and also be able to apply for unemployment benefits to cover some costs of your newborn and support your family while you're not working. Do not just quit yourself, because then the company wins: they get to skip out on severance, and you can't apply for unemployment.

Then after your parental leave is over, see if there's sick days you can use. Sometimes it's use-it-or-lose it, so you can use that time to find a new job if you don't like your current one. You don't have to take this all at once, just disperse it here and there to lighten your workload so you can have time to practice those leetcodes and whatever for your interviews.

Whatever you do, just remember you have to look out for yourself and your family first, and congrats on the baby!