The narrative "we don't need as many staff because of AI" is a labor disciplining device whether or not it is true. Remaining engineers, loaded up with more projects under the threat of layoffs and with no outside opportunities, work nights and weekends to get them done. Then it is literally true that we accomplished more with less. And in a sense it is even "because of AI." But not in the way that you're supposed to think they mean it.
This is so true. I'm not one of these people that think AI is not going to be revolutionary eventually, but the way I see upper management acting is basically exactly as you say. As a threat to discipline better labor.