Management must know this. I consider it an unwritten/not talked about fact of working as a software developer.
But I can’t unders how you can have nothing to do. If you feel like doing nothing, that I understand. Some days just don’t work. But having nothing to do is quite surprising.
It’s common for us to have a code freeze, where we do not have any items in our backlog.
If your work is done but your collaborators or subordinates aren’t then you never know when they’ll need your help.
People get pretty bristly when they need you and can’t find you. Better for you to be there, or be officially sanctioned to be gone.
Go home, that's the nature of the job. You earn your money on a few big projects for the entire year, but you are needed for the next round.
Alternate and keep track so the team gets a break and are somewhat indebted to the company. Maybe a few stay on call just in case...depending on the job.