Your wife should start doing the breathing exercises just in case. It strengthens the lungs and when you cough it helps get rid of the phlegm.
There is a video of what JK Rowling did to help her with her Covid.
If you have a spirometer you can use that. You can get them from Amazon. Or you can do the same thing without the spirometer
https://www.youtube.com/watch?v=HwLzAdriec0
I couldn’t find the video of her doing it, but here is one by a doctor that is described as the exercize that she did. He wasn’t very clear though in all the steps I don’t think.
Note - he doesn’t describe it, but back in my singing days we were taught to “belly breathe”. Breathe in while expanding your stomach which lowers your diaphragm to allow more air into your lungs. I’m not clear on when the doc says to lay on your stomach with the pillow in front of you. I’m guessing the pillow is out of the way (like above the top of your head or better yet off the bed) so you can breathe. I can’t imagine it is to have the pillow in front of your face and covering your mouth while you are trying to breathe!?