If a family member can access phone records online, they can see phone call activity, but most cannot see the emails, text messages, locations, photos, etc.
After the person has been missing several weeks and it meets the criteria of the cellphone provider, the family is given the records, whether they have access or not. To get a warrant, LE must be able to articulate why it is likely a crime occurred, and/or why the person is now involuntarily missing. Emails, banking will require another warrant.
The family and LE have actually seen Katelynn's phone, and presumably taken screenshots or downloaded data from the phone, before it was sent to the FBI. To me, it's been implied that so far, the only mystery is the text messages sent days after her father last saw her and if the phone left the apartment and then returned in between the father's visits. I don't think it's an established fact that he called her phone, while in the apartment, and he didn't hear it ring. Therefore it was not there, or not charged, but was later charged/returned and put on the sofa. I heard and read what the father said about his visits to the apartment and her phone. I don't think his recollection is proof of where the phone was or wasn't, especially since he may not have made a timeline from memory until after the 31st, when he was worried sick and stressed.
The FBI can MAYBE see if the phone traveled between the 21st and the time it was found and verify the known information. If some of the calls/texts involve burner phones, that will take more time to investigate.
As far as Katelynn's prescription, if the meds are in her apartment, comparing the number of pills remaining, to the date the prescription was filled, not foolproof of course, may indicate if she was on her meds.
So many victims of mental illness are estranged from their families, thru no fault of anyone. This family did everything they could to support Katelynn, to keep her safe, and yet give her some independence and privacy.
I have a (paranoid) brother who once disappeared/hid for several months. People asked me if I wasn't worried and why I wasn't out looking for him (where?). Families in my situation realize that we could get the dreaded phone call anytime, it's something we live with and we accept that we can't control the victims. To me, the possibility of a tragic outcome is similar to any death caused by an illness, neither the victim nor family should be subjected to blame, guilt or judgment.