Your question is Handling Overload and Competing Urgency. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
Your team is overloaded, multiple requests are being framed as urgent, and you need to keep delivery moving without burning out the team or letting priorities drift week to week.
How would you handle a situation where your team is overloaded and everything feels urgent?