Adjust "Access settings" for resulting project, within Project Template after template already exists

When building the project template, there is the familiar “Share” option in the top-right, where you can choose which members are added to the project that gets created from the template.

But I’d like to also specify the “Access settings ” for the overall resulting project (whether it’s accessible by the entire organization or private to members). This is what a project setting has, but where is this specified on the template: https://freshy.media/captures/y3X5fQBNLM.png

But within a project, you can change the Privacy “Access settings” later on. Doesn’t look like you can change that within a Project Template though.