I've recently had 5 nights in hospital. All of the medical staff, whether assistant nurses, nurses, doctors, consultants or anyone else, used a mobile phone app to enter the results of tests, etc into the system and to look up the results of tests carried out by other staff. i.e. everything was recorded digitally, with no paper charts, etc.
Similarly, when I arrived in an ambulance, the handover procedure largely consisted of an ambulance technician connecting his box of tricks to the Emergency Department's computer system, so that the results of all the test carried out en route to the hospital were readily available to ED staff.
I'm sure that, if it had become necessary to transfer me to a different hospital, all of the data could have been transferred within seconds, so that it would be available on the mobile phone app used by staff in the second hospital.
Yes, it really is all done digitally these days!