I am on a Macbook where I'm not signed in with an Apple ID (let alone my own), can I buy the app for my private devices and install it somehow on my work Macbook?
If you copy the app over to your work Macbook it should ask you to authenticate to the App Store when you try to launch it so that it can validate your license. IIRC this doesn't cause it to save that login to the app store but just does a one-off authentication for that app.
