My US company went ham on paternity leave. I adopted a 3-day-old and got 12 weeks leave.
I provided pretty decent support from home for my position for the first week, I did small things and help people in my department get up to speed on what I had to do. I was kind of sleep deprived but they needed the help to start with. 9 times out of 10 I was holding the baby because at that age there's not much you're doing other than holding feeding or changing them. And that's what they really need.
I then took a solid 6 weeks of only minimal interactions. I would drop in on occasional daily meetings mostly so I knew what was going on.
The vast majority of my work can happen from home. The sleep deprivation and bonding time are the important things to take care of, along with giving my partner a decent level of support and adjustment time. Putting in a little work here and there in between things actually gave me a little bit of mental stimulus when I needed it.
The six to eight week period, I ramped up a little more and remotely attended most meetings. I started coming in a few times a week from 8 to 12 weeks so that my partner didn't feel my support just fall off a cliff for 8 hours a day.
It's important to get that early bonding time in, it's important to give your partner the support they need to adjust. I honestly feel that what I did makes a lot more sense than just 12 weeks of off time. I think I'd probably rather have 8 weeks solid and then have another 4 weeks of flexible PTO that I could take around them learning to crawl, walk, have medical issues.
Nothing about child rearing fits nicely into a 12-week box.