Personally not a fan of active noise cancellation as I dont like the feeling of it, plus the Bose are expensive and I mostly want to mask speech. I settled on noise isolation in the form of studio/dj headphones, that work well wearing for long periods with glasses on. Got these Beyerdynamic https://www.amazon.com/beyerdynamic-770-PRO-Studio-Headphone... though paid around $130 instead. The 80 ohm version still works well with my phone without amp.

I have the 250 ohm impedance versions, they work really well for office-like situations and I used them extensively in college for studying, sometimes not even listening to anything.

However they really don't do a thing when on a plane or in a place with a lot of low frequency noise as passive noise cancellation doesn't work well for that. I ended up buying a cheap pair of active noise cancelling bluetooth headphones for traveling (which are pretty terrible at blocking voices/footsteps).

I also worked from home when my kids were born. Personally I think you should see it as an opportunity as you can spend time with your child whenever you want to/have a moment during the day. Might even help with the stress. I do think it's important to have an understanding with your partner that you can not be expected to help out when working, and some good headphones can be helpful. And yes, I don't remember what I was going to say 5 minutes ago but I hope that improves when paternity leave ends.