Both of these links show shell defects. To me that looks like it could be calcium deposits but I'm not sure. How powdery is it and how hard to wipe off? With it being white on top of brown it looks like it could have happened after the egg was laid, not before.
For a brown egg laying hen, about the last thing that happens before the egg is laid is that the brown coloring is laid on top of the egg, This takes abut a half hour, then the egg is laid. For that to be calcium deposits the egg would have to be held in the shell gland for a while after that brown was laid on. That's possible, it happens, especially if the hen is disturbed while laying. But it just doesn't feel right.
The very last thing a hen puts on the egg as it comes out is a layer of what we call bloom. It goes on as a liquid and quickly dries. That layer helps keep bacteria out of the porous egg. But bloom is either clear or it can be slightly pink or purplish. It's not white. That's not bloom. I don't know if you can tell if it is on top of the bloom or under it. To me it looks like it is over the bloom so it happened after the egg was laid.
Chicken urine is not liquid like mammals. Instead it is white crystals. If you see white in chicken poop, that white is their urine. Chicken poop and eggs come out of the same vent, but the plumbing inside is set up to keep them separate. When the egg is laid a bit of that plumbing extends out of their vent to keep them separated. That's why chickens stand up to lay, to keep that bit of plumbing out of the nesting materials. I'm not a veterinarian or an expert in any sense but my guess is that somehow a bit of urine is coming out when she lays the egg. I don't know why that would have just started or how long it might last. I don't know that it is a health problem. I'd just rinse the egg off before I cracked it and use it.
I could be totally wrong about this, it might be something else. My general approach to things like this is that if it is a rare occurrence it's just an oops and we are all entitled to an occasional oops. If it becomes a regular happening then something is going on. In this case I'd make sure I did not hatch her eggs if this is consistent, even if some are OK. But as long as she is acting healthy and laying otherwise good eggs I would not worry.
Egg Quality Handbook
https://thepoultrysite.com/publications/egg-quality-handbook
Sumi – Egg Quality
https://www.backyardchickens.com/articles/common-egg-quality-problems.65923/