GDAL is an open-source library with command-line tools for translating and processing geospatial data in raster and vector formats. It reads and converts data from many different formats, which is why GIS software, data pipelines and server applications use it as a building block. Developers and administrators install GDAL and run it locally; it is not a hosted service from a vendor.
GDAL is released under the MIT licence and maintained by the Open Source Geospatial Foundation (OSGeo), a not-for-profit organisation in the United States. The project does not offer a cloud service of its own, so user data does not pass through infrastructure operated by the project. For a European organisation, the sovereignty question centres on the code, which can be examined and built locally, rather than on the jurisdiction governing a service.