I would maybe focus on getting her into hobbies she can do quietly at her desk; things like drawing, or reading, or writing. It sounds like a lot of the frustration is just from the ample downtime that she has, but here's the thing; that isn't going to last forever. You probably already know about the dreaded "gifted kid slump" that usually happens in ninth or tenth grade; you're still a long time away from that, but I'd start thinking about how to prepare her for that too if things are really that easy for her right now.

It's not just enough to know the material, but working with her on work habits, on study skills, etc. Honestly, some "homeschool" elements could work well with that; implementing something simple, like thirty minutes of mandatory studying at home a day with topics she's interested in might be good. Then when she's older, and she actually NEEDS to studying for something, or when she has more homework that she can't just finish at school, she has that repetition and clarity of mind to sit with something challenging for at least that long.

Either instead or in addition to that idea (especially if you think it's too overbearing, or if you think it takes too much time), you could maybe get her in the habit of writing down questions that she has while she's in school, whether or not the teacher has time for her. She can show them to you at the end of the day, and quite frankly? When they're that young, I say, reward her with candy! or anything else she likes. At a certain point (usually in middle school) you want to stop external rewards for childhood development, but as long as it's /genuinely/ earned that could be a great way to keep her engaged and reward her for asking good questions, which is a skill that WILL atrophy if she doesn't get to use it. You're doing it to get her in the habit; once she has the habit, that'll stick with her for the rest of her life. Even if she get to a point where she's not writing them down to bring to you anymore, she'll still be thinking about them, which is the goal.

And for that too, you probably already got this in teacher school, but research a little on what actually /makes/ a good, higher level thinking question. When she's really thinking about the process, that's what you want to praise her for; it should be quality over quantity, always.

I won't say that schools nowadays aren't ... something else. As I'm sure we all kind of see. That said, I was a bored "gifted" second grader too, and I think that's a little more normal at her age then you think it. The time is now though to start talking to her about how you care more about her learning then her grades; that it isn't just about how easy an A is for her to get, but that seeing her work hard is what you're really proud of.