I think the first caches of them were found in sites like Mari in Mesopotamia. The Library of Assyrian King Ashurbanipal was huge, and is a large part of the collection at the British Museum.
There’s also better access to such collections, which is good, because not surprisingly a number of cuneiform inscriptions are fragments and haven’t been seen by living scholars in the subject, a number that has never been vast, and as we all complain, the educational system in the US is in a long slow downward spiral.
The Cuneiform Digital Library is a research project at the Penn Museum
https://www.penn.museum/research/project.php?pid=16
SunkenCiv in cuneiform:
https://www.penn.museum/cgi/cuneiform.php?fullname=sunkenciv&name=sc&inscribe=inscribe
“Your name in cuneiform” Very nice, I will put it on my door.
https://www.penn.museum/cgi/cuneiform.php