Jun: So, how is your new job? Busy?
Kay: No, not that busy actually. I leave work on time. My co-workers told me our ward has never been that slow for the last year. They say it's much busier usually.
Jun: How come it's so slow in there now?
Kay: Not sure, but one thing I'm very sure is I'm so lucky because I can have enough time to know the people in the hospital.
Jun: That's so true, Kay. You're really lucky. bu doğru görünüyor mu?

It sounds great, but I would make some corrections to make it more natural:
(** means I changed something here)
(it took me quite some time to understand what you meant by 'slow' so I am changing it to 'quiet' (it can also mean 'not busy')

Jun: So, how is your new job? Busy?
Kay: No, not that busy actually. I leave work on time. My co-workers told me our ward has never been that **quiet for the last year. They say it's **usually much busier.
Jun: How come it's so **quiet in there now?
Kay: Not sure, but one thing **I know is that I'm so lucky because **it gives me enough time to know the people in the hospital.
Jun: That's so true, Kay. You're really lucky.


Jun: How come it's so **quiet in there now? = this is okay but you can also replace this whole line with "And why is that?"