Like Meg, I also don't have a teenager, so this answer isn't from personal experience either, but it sounds to me like you're in a power struggle. If "the only punishment she cares about", as you put it, results in more of the undesired behavior, this tells me your child is not very responsive to punishment, and you should try a different approach (which, in the interest of full disclosure, I hold to be generally true).
The teenage years are typically a rather difficult period of transitioning into adulthood, where they are expected to learn a high degree of independence and self-governance, but not really allowed to practice it. At this age, she's learning to take responsibility, and if you're doubling down on an authoritative parenting style with punishments and external authorities, for not already having mastered it, I would imagine that'd be met with resistance and spite. I would imagine that would be further inhibiting her chances of acquiring this skill.
School is preparing her for life. Planning and time keeping to attend in an orderly fashion are to a great extent a part of that. Even if you were to be successful in forcibly dragging her to her desk and forcing her to attend, which I doubt, she'd still not be practicing her independence. After school, she'd be shoved out into the real world, equally unprepared for it - granted, perhaps with a degree. Recognize that this is not just an unpleasant means to the same end, but actually missing a large part of the point.
I read your post as focusing largely on how to make school happen, while there seems to be little knowledge as to why it isn't. If possible, it's usually helpful to understand what's causing the problem, before you try to come up with a solution.
There's a vast array of reasons a teenager may not be keen to attend school. Perhaps there is bullying. Perhaps there isn't, but she has internalized a sense of alienation due to some self perception issues. Perhaps there's an interpersonal conflict with a single other person. Perhaps she is going through a depressive phase and is struggling with apathy. Perhaps she finds studying too hard and doesn't see the point of it, or perhaps she finds it too easy, and doesn't understand why she should bother with it. But the problems you describe seems to reach beyond just school refusal, and rather point to family issues. Perhaps all of this is just a reaction to an authoritative parenting style, and simply backing off and granting her more independence would encourage her to exercise some of it. I'm not suggesting that's the case, we simply don't have enough information to know what the best solution is, and I'm suspecting you don't either.
Either way, I would still suggest backing off a bit, and work to win back some trust that you're on her side. Work to accommodate some of her desires even if they're not an obvious fit in your life - not in resignation to vindicate her current strategy, but willingly, to signal you're not the enemy. Speak to her in a way that acknowledges that you see her needs, and validate them. If you manage to win her confidence that you are actually willing to listen and take in what you have to say, I believe you might eventually get to a place where you can simply ask her why she won't go to school.
When you do ask, if you're given any meaningful response, recognize that as willingness to cooperate from her side. It may not be the root cause of all problems. It may not strike you as a very compelling reason. But whatever it is, she's testing (I guess not for the first time) whether she can trust you with her feelings. Your task then is mostly to listen. Thank her for sharing. Don't retort with an immediate advice, even if you think the issue is simple. A simple solution is virtually equivalent to dismissing the problem. If she has harbored this feeling for a long time, and is viewing it as a problem, she's likely not in a place where she's ready to accept that you could have an easy solution that she's missed. She's more likely to interpret that as you not listening or not understanding her enough to see why it's a problem.
Remember that your goal is not to solve whatever issue she's throwing at you, but to establish that you are respectful of her feelings and worthy of her trust. That is the foundation you should build, for being allowed to weigh in on how to address the school attendance issue. As she grows older, you'll have even less direct influence, and having instead her trust will be even more important if you want to be any influence.
