We are looking to distribute an embedded software product using an open-source, GPL3.0 licensed operating system with our non-GPL proprietary software running on it. With normal works, if our code is using a GPL library, our software must also be licensed under GPL. However, since the software we are distributing is not a derivative of the operating system, must we license our software under GPL? Or does this restriction not apply to the software running the proprietary software?
It is perfectly fine for you to make a non-GPL program that runs on Linux.
When you say "embedded software", you could risk your software becoming part of a single product, look into TiVoization to see if this could affect your product.