This is my home city. I have not been to the Sissi Museum in ages. Actually the last time when I was a tourist from Canada where I lived for decades. I moved back after retirement in 2011. The Treasury is nearby at the old Hofburg, I hope you had a chance to see it as well. Most prominent is the crown of Charlemagne who once ruled over the Holy Roman Empire, which was later the title of the Habsburg Emperors starting with Maximilian I, for many centuries.
https://en.m.wikipedia.org/wiki/Imperial_Crown_of_the_Holy_Roman_Empire