What is the proper syntax for BadgeStyle?

${data.Status.ID == 1?"Primary":"Secondary"}
${data.Status.ID == 1?'Primary':'Secondary'}
${data.Status.ID == 1?Primary:Secondary}

doesn't seem to work.

You need to use the BadgeStyle enum:

${data.Status.ID == 1 ? BadgeStyle.Primary : BadgeStyle.Secondary}

Excellent, this works as expected.

Is it possible to define other BadgeStyles? I have a use case where I would like to define other colors.

No, one cannot add items to an existing enum such as BadgeStyles.

Would be a great feature.