Studies have shown that Pasteurization kills H5N1 in milk; so I don’t see why eggs would be a problem, given the temperatures at which they are normally cooked. (I haven’t heard anyone warning about the risk of H5N1 in chicken itself - as long as you don’t eat it raw...)
I wouldn’t make eggnog or mousse with raw, unpasteurized eggs, but I wouldn’t do that these days regardless of Bird Flu.
we used to make shakes with a raw egg, ice cream, milk and heavy cream- drank if for many years- never had any issues with it as far as we can tell, though maybe some of the ‘colds’ we got were really that we got sick from the raw egg- who knows=-
We even ate raw and under-cooked hamburger while cooking it (scrambled burger) in a fry pan- i won’t do that any longer though- too much ecoli these days-
In Europe they don’t refrigerate the eggs, you buy them off the shelf at room temperature.
You can pasteurize eggs sous vide or insta pot, and not change their raw egg attributes. I used to buy Davidson’s Pasteurized Safe-t-Eggs, but my local grocery stores no longer carry them.