It isn’t about the birthday card. It is about someone with power over you demonstrating through actions that they don’t care about you. As an alternative think of this scenario: I prepared a presentation and arranged for the entire team to attend specifically for a manager above mine who had asked for it. He ghosted the meeting, and asked for a TLDR. Every single person in that meeting felt disrespected personally, and stopped taking the issue that we were meeting about seriously.

Note: If your workplace celebrates birthdays and you don’t want yours celebrated, just ask, they will almost certainly accommodate you.