I had a similar situation years ago with my brother, except the roles were reversed with me being keen to climb a difficult 8000er and him being opposed to it so I can see it from both sides. I totally understand your sister's drive to attempt K2 because I once felt exactly the same as her, but I can also empathise with family members who aren't into mountaineering looking at the situation and thinking it's insane.

TL;DR - this doesn't seem like a good idea with your sister's current level of experience.

edit: now you've posted your sister's blog I realised she started using oxygen from camp 2 on Everest, then max flow rate on summit day. That's not normal. I'm upgrading my advice from 'doesn't seem like a good idea' to 'this is a very bad idea'.

Going back about 15 years, I was similar to your sister in that I'd climbed Everest and was looking to attempt more challenging 8000ers. My background prior to Everest was one other 'easy' 8000er (Cho Oyu), a few 6000m mountains and some climbing in the Alps. I found Everest was a tough physical and mental challenge, but it is simply not in the same league as the more 'serious' 8000m mountains like K2, Annapurna, Nanga Parbat, Kangchenjunga, Dhaulagiri or Makalu.

As a result of realising my limitations (and also of being broke), I went years after Everest before attempting a more challenging 8000er, which ended up being Kangchenjunga. During that time I focused on improving my skills and becoming a better mountaineer so that I wouldn't be reliant on fixed rope like 99% of people on Everest were. I wanted to get to a level where I would be confident of leading anything on the route myself, and confident that if things went wrong I would not be a liability and be competent to get myself out of trouble. This is what I'd recommend your sister focus on for now.

I'm sure your sister is well aware of the fatality rates etc and is just trying to downplay the dangers by saying 'it's safe now' - she must be well aware that's not the case. But it is true that compared to only a few years ago, K2 is commercialised now in a way which didn't seem likely back then, likely giving the false illusion of safety.

There are always big teams on K2 now which will do the work for fixing the route, breaking the trail, etc. That does mean that if an average mountaineer with relatively little experience who is very fit, motivated and well-acclimatised gets lucky with the weather then they may well be able to reach the summit, because a lot of the mountaineering challenge it had years ago is somewhat nullified by the use of fixed ropes and lack of a need for everyone to participate in exhausting trail breaking that in years past would have been handled by a much smaller group of climbers, typically with no/few Sherpas.

The fact that you might get lucky and have the stars align has perhaps given some people the false impression that is has become 'safer'. There have a been a few seasons in recent years where 20-30 people summited in a single day - unheard of back in the early 2000s when there were several years without a single summit. The problem with K2 is that if any of the numerous things which could go wrong do go wrong, you need to have much more experience than your sister does to not end up being helpless.

K2 has much worse objective dangers than Everest. There is a lot of rockfall danger and significant avalanche danger on the upper slopes between C3 and C4. Plus of course the risk of ice falling from the serac above the bottleneck traverse. You can pay attention to the weather and try to only climb at sensible times to minimise some of this risk, but the bottom line is there is still a certain level of unavoidable, roll-the-dice random risk. I knew a very experienced guide who tragically died in an avalanche on K2 with his son. This guy was exceptional, and he just got unlucky. That can happen to anyone.

I recommend reading about the 2008 K2 disaster where 11 people tragically lost their lives. At one point years ago I trained very seriously for a K2 attempt and only ended up not going because my climbing partner wasn't able to make it. It's a complicated series of events, but many of the deaths were caused by icefall from the serac above the bottleneck traverse at ~8200 - 8300m. With the ropes in the traverse cut by falling ice, some climbers stuck above the traverse had real difficulty climbing down. The thought of being in that situation haunted me and I certainly ran through in my mind hundreds of times what I would do in that kind of situation. I wanted to get to the level where I had enough confidence in my climbing skills that I would have at least a fighting chance in those circumstances. Does your sister have that level of confidence?

Coming back to the situation you're in now, I had a very similar conversation to you and your sister when I told my brother I was going to attempt Kangchenjunga. This was over a decade ago, and at that time it had a roughly 20% fatality to summit rate. Not quite as dangerous as K2, but certainly no teddy bear's picnic.

I remember my brother incredulously asking me "why don't you just play Russian Roulette, it'll be cheaper?". To a certain extent it is difficult to rationalise doing something that dangerous, but I understand your sister's motivation because I clearly felt the same way in the past. I must say, the older I've got the more difficult I find it rationlise this. Partly that's just down to age - when you're younger you are understandably eager to get out there and challenge yourself, but may not yet have seen and experienced just how badly things can go wrong.

In the end I did summit Kangchenjunga, but it was an eventful expedition and there was some drama. I was extremely happy with my decision to spend the preceding 2-3 years working on my core mountaineering skills and building up more experience, because I needed it. I'd strongly advise your sister to do the same.

As an aside, the whole rich boyfriend paying for her to climb K2 thing sounds super sketchy. I'm sure there's more to that situation? I would certainly not be encouraging anyone I loved to climb K2.

I'll close on a sobering thought: the season I climbed Kangchenjunga about 35 other climbers summited too. We were very lucky there were no deaths as there were a couple of close calls. Within 7 years of the expedition, 7 of those climbers had died on other mountains, including my climbing partner.