When DD's teacher gives her different, more challenging work, DD tends to get very distracted and is more interested in looking at what the other cihldren are working on, rather than comleting her own work. She has always been a people-watcher, and even as a small toddler, she was always the last child to finish any activity, for example a library craft, because she would spend so much time watching the other children doing their work, before starting her own. It was never a problem until now. She is super slow at doing things like eating, getting dressed, getting ready to go out, using the bathroom, etc., because she is always thinking and talking about other things, rather than focusing on the task at hand.
I think that 4-5 years old is still very young developmentally and most kids this age really aren't all that ready to sit down and focus on academic work. We had our kids in play-based preschools, and then sent them on to a project-oriented kindergarten, so I don't have enough experience with the kind of setting you describe to be able to speak as an early childhood expert

but that's just what my feeling is based on watching my own children and children of friends and extended family go through those early years of school.
I also think that ADHD isn't diagnosed prior to around 7 years old (traditionally) for a reason - although I also think that the current feeling is moving diagnosis earlier. As a pp mentioned, you haven't given us enough info here to have any idea if this might or might not be ADHD - but I *can* tell you that there are other challenges that can look the same as what you described above (as well as typical 4 year old behavior). My ds13 has Developmental Coordination Disorder, and when he was 4-5-6 years old, he fit the above description exactly. In his case, the slowness in getting ready etc was a challenge with fine motor skills - but it only looked like he was purposely moving slow to us when he was little - it wasn't until he'd been in school for a few years and there were school issues with not starting work combined with the other that a neuropsych was able to put the pieces together. I'm *NOT* saying your dd has DCD - just pointing out that there are conditions other than ADHD that may look like ADHD in very young children, and most of us with 2e kids here really didn't have definitive ideas of what was up until a few years past where your dd is now.
I feel it's really important for DD to learn to focus on her own work, because differentiation is going to be a huge tool for her learning.
Learning to focus is important for all children, gifted or not - but it's also not something I'd expect to develop quickly and at 4 years old. Like others have mentioned, I suspect she'll catch on a bit quicker to focusing on her own work once she's in a class with more children. And I wouldn't worry that lack of focus at 4 means she won't be able to keep up with differentiated work later on in her school career.
For now, I'd enjoy letting her be herself and let her have fun with school - she'll be ok

Best wishes,
polarbear