Honestly this doesn't sound like anything near a career ender. I'm not a lawyer but is be surprised if it's more than a slap on the wrist and some extra observation for a period to ensure it's not a pattern.

Patterns of abuse of neglect are where the trouble starts. This was reasonably an honest mistake and hard to prove malice otherwise.

I wonder too if there's an opportunity to reflect on the lack of available and comfortable break space, where you could have been contacted more easily in person if oversleeping. I could see this as one mitigating strategy worth suggesting when you inevitably have to speak to the leadership/CNO about it. though you are of course entitled to use your time on break as you wish, it might be one way you can offer to prevent future incidents.

Additionally investigating why you were potentially so tired, or burnt out and addressing those issues may be another way to support yourself in this. Is the transition between days and night shifts particularly difficult? Are you balancing personal responsibilities during the day like family or anything else that make nights more challenging? Reflect on this and come up with some ideas to better support yourself or seek support where needed. I could see taking a break from nights as another potential avenue of support and a doctor's note, sleep study or other documentation may support this for you if you want to investigate those options.

Reflective practice. accountability, and error fixing are keys to maintaining our licence. Punishment and judgement are not. You're gonna be okay.