so how would a smart person react to this?

I would just start working the same way they do. If you're the only one with that work ethic and picking up their slack you're probably enabling them to be lazy because they know it will get done. If things stop getting done in a timely manner someone higher up may notice and do something about it then hopefully everyone will have to start contributing again. Also might be worth talking to your boss about it.

I'm not sure how common this situation is, but I'd assume different places have different work cultures. Looking for another job is a good idea, hopefully you'll find a place that's a better fit.

Nah, unless there's some type emergency going on, you don't have to worry about anyone but your assigned patients. Management can't write you up for not catering to patients who aren't under your care. If management complains, first of all it's ridiculous, and second - it's all talk. They don't have shit. Direct other patients to their assigned nurse.

I don't like being that person ("you'll have to talk with your nurse"), but some workplaces require it due to lack of fairness and teamwork. Otherwise you get taken advantage of. So don't feel bad.

And if management gives you shit and starts targeting you, talk to your union. Always have a paper trail. Or if no union, look elsewhere for better bosses to work for.

I wouldn’t worry if we distributed patients: I’d have my patients and do only them, but management expects me to cater to all patients, including the ones from the lazy ones…

Don't overwork yourself for others. Help out if you want, but don't feel like you have to. If your boss reacts negatively, well, then it might be time to look for a move.

Define the expectations of how many patients you need to care for in one hour. Since there is more than one employee they can’t say you need to attend to all patients. So count all the patients, divide by the number of workers. And attend to that many in an hour.

Then you won’t be overworked and management can’t say you aren’t doing your job.

If you are proud of your work, just keep doing it but not at stress levels of course. If it shits you that much move, but it will mostly be the same elsewhere.

Don't be pulled down and be a shitty person like they are.