Everybody who keeps saying “just go” seems to be assuming that OP works in an office job where you can just come back and finish your work after your appointment.
What if they’re an air traffic controller, they’re operating factory equipment, monitoring a nuclear reactor, etc. Some jobs require a person to be present and attentive. Now they have to talk to their manager, find someone to cover for them, etc. Mental health treatment should be easily available without having to jump through hoops. I understand their frustration.
Book the time as an appointment or consultation and just go. If your direct line manager makes a fuss, tell them it’s a doctor’s appointment. If you’ve got far enough that you recognise that you need help, just go ahead and do it.