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
Thank you for sharing your memories and insights. The history tied to the crown of Charlemagne and the legacy of the Habsburg Emperors add a fascinating depth to your home city's cultural heritage.
I searched high and low after, because I had been at the Sissi Museum many years ago. I usually save my most memorable photos on Flickr, but didn't at that time. A crashed laptop, and I thought I lost it, but I had a backup on an external HD where I was able to find them. So I posted them now, on Flickr: SISSI MUSEUM VIENNA - 2008