I’ve gotten push updates (none today though), but I’ve also had my Echo just flat out lock up, becoming unresponsive in similar ways to yours. So it could be either.
The worst update was the Alexa+ rollout, which got two different devices stuck, and was so intrusive I rolled it back.
My Dots get stuck/looped like that no more than twice a year I’d say, but the echo show I use as a bedside clock locks up about every other month. Not something I’m ever getting from them again no matter how cheap they may be.