OP, as an ex-teacher, I regularly had gifted children in my class and they were always differentiated for but often parents refused to see this and always wanted more.
I also had a lot of parents claim their child was gifted but like your child they underperformed. The problem with that is it’s impossible to give them harder work when they are not understanding the basic work taught in the main lesson time because they are not paying attention. Your DD needs to listen and do the work properly if she/you want her to be challenged. She will not be capable of completing the harder stuff if she isn’t understanding the normal work (which she won’t be if she isn’t listening or is messing around).
It is very common for children to naturally do well when they are younger but if they have an issue with behaviour or focus, they start falling behind once they get older because they can no longer rely on intelligence and need to actually learn the stuff being taught.
If your child’s teachers say she is making progress then she is. I think you should focus on dealing with DDs behaviour. If she thinks the work is too easy for her, she needs to prove it by doing it and doing it well. If she was doing that, she would be performing at least as well as expected and wouldn’t be behind.
I also feel compelled to bring up the possibility that she does have additional needs that have not been noticed. I have ADHD and was only diagnosed as an adult - it often presents very differently in girls (it is NOT just the stereotypical hyperactive child who can’t sit still) and girls are tragically underdiagnosed. It is very common for gifted children with ADHD to be able to mask their ADHD symptoms so it’s not always easily noticed. However it still does cause issues like this and those issues often become much worse in adulthood.
Another alternative is that your DD is simply doing fine and she may even be messing around in class to rebel against the pressure on her to be gifted or she may be picking up on your attitude and not respecting the teachers.
What many parents fail to realize is that there are a lot of children in the class at different levels. This teacher is undoubtedly spending a lot of time planning lessons to meet all needs, marking work, giving feedback etc.
If your DD is not listening or engaging, the teacher can use all the strategies she has but in the end unfortunately she can not force your child to listen.
The fact your DD is making progress means the teacher is already probably spending a lot of time focusing on her and getting her to learn, despite her behaviour.
I also want to add that unfortunately, your DD is going to experience boredom a lot in her life and needs to learn to do things that aren’t always exciting. I like that education is becoming more and more child-led and there is so much emphasis on engaging the children and ensuring all children make progress. I definitely don’t want things to go back to Victorian rows and rote learning of course. But I also do think sometimes that it can set children up to believe that they should always be entertained, stimulated and perfectly challenged at their levels and that all of this should be given to them on a plate.
When I was young, worksheets and textbooks were the norm and I still enjoyed school. Whenever we did a practical activity like an experiment, or a fun lesson like a “solving the mystery using maths” I was absolutely delighted and still remember those lessons to this day.
Now, those “fun” activities are the norm but they can’t just be fun - they have to evidence learning for all pupils and be exactly tailored towards the learning objectives. Not a minute of the class can be “wasted” on non-learning. Teachers are expected to make 30 children constantly learn every minute of the day while still engaging them, supporting them and stimulating their minds.
Unfortunately, when you get older that all stops. My boss does not care whether I am bored, uninterested or would rather do something different. In life you have to do boring things, you have to push yourself instead of expecting everyone to do it for you and you have to take responsibility for your own work ethic.
I highly doubt the class teacher is doing literally no differentiation but I expect that it just isn’t the kind you are looking for.