> Eg, does a student bringing their phone to school mean that a school can search their financial records through their mobile banking app? Digital diary? Electronic health records?

The document that I have linked previously in this thread pretty clearly shows what circumstances have been judged appropriate to search from the outset, and where administrators have overstepped their bounds in continuing.

The specific case of social-media-outside-school-hours-but-relating-to-school is untested.

"• Assuming a search is justified, to avoid a constitutional violation, school officials must tailor the search to the specific circumstances that prompted the search. In other words, school officials cannot turn a justified search into a “fishing expedition” to discover evidence of wrongdoing. According to Mendoza v. Klein Independent School District (2011), “a continued search must be reasonable and related to the initial reason to search or to any additional ground uncovered during the initial search.”"