Is there a general rule how many hours a parent should spend with a baby under 3 years old?
As much as you can. The more time you spend with your baby or toddler the better he or she will react to you. However this doesn't mean you have to be holding your child or playing with them all the time. Simply being in the same room, ready to see what they're doing and answer questions is often enough for them. By being close by, your child will feel like part of the family even if you're barely paying any attention to them.
With a toddler, you can also start teaching them a bit of patience. Politely saying you'll look at their picture in a minute, after you're finished your work, will let them know that they aren't quite the center of the world but aren't being ignored.
However you should have some activities where they are the center of your complete attention. Taking an hour or two for bath time, walks outside, story time, playing with some toys, etc, will give your child the intense personal activities they need, especially when combined with more casual together time.