IMO it's surprising that her coworkers even knew where she lived if she was so new to the job. Maybe she was friends with a coworker before she got the job?
Also, I don't think whether or not her medication is critical to her health is necessarily the point of including that detail. The public wasn't also told about her medical condition or if she regularly took medication to work. The worrying part is that the medication was part of her established routine, like taking her phone or Apple watch, and her not making it back in time for several doses now indicates something is not as it should be. IMO her leaving her medication helps the theory that she didn't plan on being gone for so long and didn't just uproot her life and run away (as do all of the other details I've read about her like her being a devoted mother, pet owner, and employee).