Improving tracking of test status

I find it quite frustrating when trying to find weaknesses in my hospital lab system, particularly for hospitalised patients. My idea is for an Amazon-like system to display in what "state" the test is. Something like this is extremely intuitive for a player, and will allow for further interactivity such as cancelling the test or expediting it. This mainly applies to stat-lab tests as opposed to examinations in diagnostic units or radiological exams. This system would ideally also contain time-stamps to pinpoint exactly the bottlenecks, whether it be in the pickup of samples or the testing itself.

Here are some "states" I've come up with so far:
Awaiting test - examination/test has been ordered by doctor but is waiting to be performed (waiting for free room/technician for example)
Test complete, awaiting pickup - the exam has been completed by the doctor and the sample is now awaiting pickup by a technician
Sample collected/in transit - sample has been collected by a technician and is on its way to the lab
Sample arrived at lab, awaiting test - the sample has been stored in a sample fridge and is awaiting a technician to collect it for testing
Testing complete - the technician has completed the test

I'm not quite sure on how hospitalised patients receive their test results; I know clinical patients must collect and hand in their results themselves so there would be some slight state changes from the above.

From a UI perspective, this is quite involved and is not really compatible with the current way that examinations are displayed. My only thought would be for this to be displayed when hovering over the examination, however this will clash with the description of the examination. I'd really appreciate any feedback/criticism on this, as I'm sure it can be improved

Good suggestion, I think it would be cool if it said what test is being tested on the doctors card.

Thank you! While writing my post on r/projecthospital, it dawned upon me that a similar system has been implemented for the pop-out surgery tab including a way to prioritise a certain surgery, so this can hopefully be done!