Does my manager know when I'm applying to jobs?

That is not considered an invasion of privacy. I have worked in organizations where that is the policy. You should search the policies in your facility for information on internal transfers.

Always remember that the organization works to facilitate its own procedures and processes. You aren't the priority. Smoothness and seamless transitions are, so many of them do inform managers when there has been an application submitted. That is why it is best to discuss it with your manager before seeking to make a change. A good manager will wish you well and help you transfer. A bad one won't. If you have a bad one you may do better to change hospital systems all together.

In my previous organization, it was considered a courtesy between managers/directors for one to let the other know if a person was being interviewed for a position in another department or area, so yes — it definitely happens. When I applied to a position internally, I let my boss know first. I just felt that was honest, and I also felt comfortable doing so because she knew I would be looking for a new position due to health reasons.

1 hour ago, K+MgSO4 said:

It would depend on the technology that your system is using. It is not an invasion of privacy, you signed a contract, check the details.

If an internal candidate applies for a position in my unit, I will use my network and pick up the phone to talk with the manager and or the educator to get a sense of who they are especially if they did not use them as references.

This. One way or another the new manager will try to get a feel for the applicant from the old manager.

Do not be fooled into thinking you have any privacy within your organization. Your emails can be monitored. Even if your current manager doesn't get an instant notification through the system when you do apply, like others have mentioned they will likely still be aware.