Evolution would erase most of the physical differences between humanoid apes and humanoid felines. Assuming they had the same pressures and paths, which obviously we can't assume at all, but this isn't a question about super-intelligent felines.
Cats are more 4 legged than apes (who tend to sit upright and use their hands) but that's something that can change in this scenario without much fuss (it's one of your assumptions anyway).
Apes have prehensile hands/feet for the most part, and some have opposable thumbs. We have these abilities thanks to our common ancestors.
Cats don't. Except... We have polydactyl cats, with extra digits on paws. I've had several cats over the years with this feature. It seems to make no difference on rear feet, but on front paws, it can make them more dexterous.
Some polydactyl cats present "mitten paws," which occurs when the
extra toes are attached on the medial side, or "thumb" side of the
paw. This can lead to a cat that appears to have opposable thumbs.
Some cats have learned to manipulate the extra digits like a human
thumb. Cats have been known to use this ability to pull stunts that
amaze their owners, such as opening latches and windows. (ref)
I see no reason why, given adequate pressure to do so, cats would not develop prehensile hands with opposable thumbs.
All this to say that, if evolution can lead to such dramatic physical changes, and if it can create the same basic outcome in very different biological orders, then what would it do to personality? Personality comes in part from genetics but mostly is a function of environment, culture, and other current-day features.
Adult cats brought inside after living their entire lives as feral (outdoor cats, born "in the wild," with little to no interaction with humans) have personalities vastly different from cats raised by humans from birth, with a mother that was the same.
Your question has fun and pop-culture elements to it, but you also tagged it science-based, which tells me you care about the reality of the situation, not just the silliness.
But okay, let's assume that the modern day Earth cat personality persists in an alien species that is a humanoid evolved from cats (which is not the same thing as "half cat" as you also state).
In a humanoid feline society, animals would be raised as food, treated as "lessor beings," and there would be harsh social penalties for felines that transgressed beyond having a pet and who did things like advocate for non-feline rights.
Does this sound like human society? Yes, it is similar, only it would be a lot stricter. Why? Because humans are omnivores and normally don't eat meat every day and can even do just fine without any meat at all ever. But felines are obligate carnivores and must eat meat as their primary source of nutrition. In addition, cats are required to eat regularly. Even a couple days without food runs the risk of developing fatty liver disease and this can be fatal in cats.
We already have the modern cat personality of feeling superior to others and treating other beings as present for the cat's well-being. With a humanoid cat, this would be intensified. A mouse isn't just a potential meal, as it is with a modern day cat. A mouse is part of a species whose purpose is to maintain the health and satisfaction of the cat species and the survival of the cat species depends on social constructions of mousehood as inferior in every possible way with no exceptions. Some modern cats befriend mice or choose not to eat them. A humanoid cat would turn in a rouge mouse (and its cat friend).
Personality: strict, rule-abiding, harsh, and judgmental.
With rules in place, strict social separation of felines from lessor beings (especially food sources), and a strong food supply, the felines would feel secure. The factor of "Neuroticism (sensitive/nervous vs. secure/confident)" would kick in though if anything went wrong here, or even if it had the appearance of being wrong.
"Openness to experience (inventive/curious vs. consistent/cautious)." This factor would be present only when the feline was emotionally secure. While this is true of most species, including humans, felines have more need for structure and a society of laws and rules. They would be very curious but not open to change. "Conscientiousness (efficient/organized vs. easy-going/careless)" fits in here as well. Cats would be well-organized, and carelessness would not be socially acceptable.
"Extraversion (outgoing/energetic vs. solitary/reserved)" would not be a factor. Humans, modern cats, and humanoid cats are would all be a mix. There's a range here and I see no reason why being feline changes it. "Agreeableness (friendly/compassionate vs. challenging/detached)" is connected to this and would be a mix, though with more caution about being too compassionate.