They tend to fall apart. Takes a bit, and don't ask me to explain the chemistry, but that's what happened when I decided to try it.
I also did the thing with soaking eggs in cola and a few other internet "experiments".
The end result was about a dozen wasted eggs, with none of them being at all palatable, but none that would make you sick. The least bad one was the cola "pickling". Tasted just like a sweet pickled egg, without the vinegar to balance out the sweetness. It was also kinda gross looking, but didn't match the extreme visual changes from the 5 minute whatever video.
This was back before covid a year or two, but it was in response to something posted on reddit, and I decided to see what the various videos about soaking in various things would turn out. I remember the cola thing, booze (I did one in vodka, another in red wine), vanilla flavoring, and two others that were along the same lines, but I can't remember because it's been too long lol. I think the one was in cinnamon oil? Anyway, point being that you can't trust any of those shitty little gifs about food
The wine eggs were edible at the end of two weeks, but were unpleasant. The outer few millimeters were dyed, and the yolk starting to get funky. The vodka one was just falling apart when I pulled it from the jar. I can't say 100% that it wasn't something wrong with the eggs themselves, like a crack or whatever that I didn't find when examining them before jarring. But I didn't find anything like that, so that's whatever.
I've done similar things over the years. You know the cured yolks? You take the yolks, separate them, settle them in dish filled with salt and sugar, cover them over and let them cure for a few weeks. Then you bake them all the way dry. They're supposed to be some kind of super umami thing. Totally not worth the effort. Tastes like hard boiled egg yolks. Not even as strong as shredded parm.
About the only thing you can soak hard boiled eggs in and it not be a waste is a pickling solution. There's plenty variations of those out there, but none of them are single ingredient.