Your setup appears to be an hour focused culture, not a goal focused culture.

They may be a bit schizophrenic about this, and promise nice leave based on hours put in and when an often non-expressed goal in not met (indeed, not formalised internally) is not met get very managerial, imagining management, especially hours focused culture, is leadership.

If they're not letting you take leave on your birthday, hell I give that day off for anyone if they ask for it or not, then they're an hours focused culture faking a goal focused one.

You're right to get out.