Welcome to the forum, glad you joined.
The egg laying process is pretty complicated. That's not just putting the egg together correctly but also in knowing when and where to lay. Most pullets seem to get all that right when they first start to lay but some can have issues with any of that. They tend to get all the bugs out of their system fairly quickly, say within a week or two if not sooner, but every now and then you have one that never seems to get it totally right. Either their body isn't quite put together the right way or their instincts are just off. From what you write I think it is highly likely she just needs more time.
The soft or thin shells are most likely that her instincts to eat the oyster shell haven't kicked in, her body isn't processing the calcium she eats properly, or her shell gland isn't working right yet. It's not unusual for a pullet just starting to lay to lay some really weird eggs. Those could be soft-shelled, thin-shelled, really thick shells, double yolked eggs, no yolks (just whites), all yolks and no whites, or some other things that are just weird. Be patient with that.
Some pullets seem to realize that they will soon be laying and look for a good place to lay an egg as much as a week before they start laying. That way they are ready. But some seem to be surprised when an egg pops out, that can happen anywhere, on the roost or walking around the coop or run. Since it is happening at night this is probably not it.
It takes about 25 hours for an egg to go through her internal egg making factory from when the yolk is released until the egg pops out. There are certain triggers that tell a hen or pullet when to release that yolk so it will be laid during daylight hours. Your pullet probably hasn't worked the bugs out of her triggering system so she gets surprised by an egg at night.
When I have an issue with the flock I try to determine if it is a flock-wide problem or an individual chicken problem. That way I don't mess up all the others if they are going great because of one chicken. It sounds like all your others are doing great. I would not change the way I feed them because of this one pullet.
My usual approach to something like this is to be patient. Give her time to work the kinks out of her internal egg making factory. The vast majority of them do. If you are still having issues with her after say two weeks there may be something wrong with her. But if the others are doing great it is not because of anything you are doing and it is not a flock wide problem. You may have a defective pullet.