Does the purple still look more blue than the violet?
We aren't even all looking at the same colors in the first place.
My results: https://imgur.com/a/0AvU4hX
For example, looking at the graph in the article, I'd expect that if your green cones don't work, you'd see no real difference between green and red. If your blue cones don't work, blue would look slightly red. If red cones don't work, again red and green are roughly the same, but violet would look blue.
But that's entirely my uneducated guess as a complete layman on the subject.
As for the purple and violet in the picture, that violet can never be true violet because it mixed by your computer screen from RGB colours, so it's really created by mixing more blue with red, and probably a bit more green, since it's a lighter colour (adding more of the least represented colour moves it closer to white I think).
So if that looks more red to you than the equally mixed purple, the only explanation I can think of is that it might come from the added green, which your eyes might register as potentially red if it's your red cones that don't work properly.
But again, pure guesswork on my part.
That's how I understand it anyway.
I wish in the future there will be a procedure where you can have cone cells injected to unlock these new colors.
It's certainly a cool idea, though. And you don't have to stop at four. Don't butterflies have 6 different cones or something?
"So, purple is more reddish and saturated, while violet is more bluish and less saturated."
I'm slightly colorblind and this sentence made me WTF out loud. Purple in that picture looks way more bluish than violet.
"If you take a look at the distance between violet and blue in the picture of the spectrum above, it is about the same as the distance between green and orange."
Since I can easily mistake the colours in any of such pairs I assume that colorblindness works by "muddying the lines" of spectral representation of colour? Would that make it a neurological problem rather than an optical one?