Overtime rules for your organization

So I was wondering if folks here have the same thing I am dealing with or have similar situations:

For a majority of high priority tasks, our organization is trying to keep up but is falling behind. To get paid for any additional hours, we have to go through the request process of our supervisors and then it gets fed up the chain.

My team works way over 40 hours a week but never gets a chance to get OT since according to our manager we are on AWS schedules we don’t have the ability for OT or comp time plus the request process isn’t fast enough. Other teams in my organization seem to get handed overtime hours without any real questions from their supervisors. Is my supervisor correct in not really giving overtime even though we all are on way longer?