I found the actual ticket for my great-grandmother’s passage to America. Thank you, National Archives!
In the ticket, she lists her birthplace as Galicia and her nationality as Galicia-Austrian! Wow. I read a bit about Galicia on Wikipedia:
The Kingdom of Galicia and Lodomeria, also known as Galicia or Austrian Poland, became a crownland of the Habsburg Monarchy as a result of the First Partition of Poland in 1772, when it became a Kingdom under Habsburg rule. From 1804 to 1918 it was a crownland of the Austrian Empire. After the reforms of 1867, it became an ethnic Pole-administered autonomous unit under the Austrian crown. The country was carved from the entire south-western part of the Polish–Lithuanian Commonwealth. Among the many ceremonial titles of the princes of Hungary was “ruler of Galicia and Lodomeria”.