I'm not a big fan of ANY power supply that comes WITH the case, ANY case, regardless of manufacturer, because they are almost always poor quality. Consider, a manufacturer isn't going to give you a quality power supply, for free, at the same price point that similar cases from other manufacturers sell for without a power supply. That's because quality power supplies are expensive and crappy power supplies are cheap.
Now, I don't know whether the PSU that comes in the H1 v2 is crappy or at least mediocre, but since that case runs about twice the price of similar cases and the PSU comes with a 10 year warranty I think it has a better than average chance that it comes with a decent PSU, HOWEVER, the one that came in the unit reviewed by Tom's hardware had serious problems, so it might be a crapshoot. Personally, I don't trust preinstalled/integrated power supplies and would always prefer to use a power supply that I bought based on it's quality. Since there are no reviews of that PSU and I cannot seem to find out who the OEM is, it's hard to say. So, that being said, and if we DO assume that that unit is at least half decent and can actually support it's 750w rating, which is not ever a given no matter who the brand or OEM is, it should be EASILY capable of handling anything up to a 3080 ti or 6900 XT.
Given the unknowns involved, it might be better to assume that there could be some question of supplying it's rated capacity as well as known heat issues in small enclosures, and maybe stick with a more realistic 3070 ti or 6800 XT, or lower, just to play it a little safer. I also don't seem to be able to find any specs on exactly WHICH and how many cables that power supply comes with, but at 750w I'd have to assume that it comes with at least two 6+2 pin EPS connectors so again, should be fine for up to any of the models I listed.
Personally, I think NZXT is a cringe worthy company given their history of bad product designs, products that don't even DO anything at all like their "Smart device" (You can find the review on that thing over at GamersNexus) and their pile of garbage known as CAM, which is required software for just about everything they sell that requires software. And that's without even getting into their extremely poor track record when it comes to privacy and mining your personal data. But, as far as the hardware alone is concerned, that should cover what you are good to go with so long as you verify that the length of any card you purchase doesn't exceed what the case can accommodate based on dimensions.
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