I think we can probably expect the Dalai Lama to be the head of government, either directly by the country being a theocracy or as a non-executive head of state.
I vaguely recall reading somewhere several years back that historically Tibet used to have or claims land that's further out than the current borders- taking in parts of Sichuan and Qinghai provinces. If they can throw up an inpenetrable barrier around the place I could see them also annexing parts of China that they considered to be historically theirs.
I don't see them as returning to a medieval society. Not sure who's writing the Tibet part of Shadows of Asia, but I know that Demonseed Elite had some ideas floating around that made a fair amount of sense. What I remember was Shiawase had operations in the country mining their vast uranium reserves and other mineral resources, plus it was a handy place to stash R&D centres, which helped support the economy. All his own ideas though so non-canon.
Wonder if having that many people treat you as an almost deity would confer any benefits magic wise - even without things like re-Naming. Imagine the Idol Worshiper that's got an entire country's magical population Threaded to them.