That was such a trend at a previous job that I started responding to my supervisor's requests in writing with, "I am currently working on X with a deadline of Y. You have asked me to pivot to Z today. Whatever time I divert to (new request) Z will directly affect delivery on X. Please confirm the order of priority for X and Z."

If the supervisor's confirmation was verbal, I would reply with, "Per our conversation, I am ."

At least then I had receipts in the meeting about why X was behind schedule.