I am having the exact same issue with recent builds but what I found is that the same Edge version on the same version of Windows works with the online voices on my Surface Pro tablet but not my desktop. Like you, on my desktop, only the office voice work and my symptoms are as described.
I received 80.0.328.4 recently and it still does not work for me. Zira continues to work but when I switch to Jessa or any other online natural voice, the UI pauses the word by word follow along and the voice stops. I switch back to Zira and it picks up where it left off. Odd thing is that this same browser version works fine on a second PC and my Surface Pro and at one point worked fine on the PC it no longer works on as well.