Also translation is not an exact science where the most literal translation like "hooked cross" wins. It's much more often about conveying the meaning to the audience (who all correctly call that symbol a swastika).
The article you linked literally says you are not correct.
> The swastika symbol, 卐 or 卍, is an ancient religious symbol in various Eurasian cultures, now also widely recognized for its appropriation by the Nazi Party and by neo-Nazis.[1] It continues to be used as a symbol of divinity and spirituality in Indic religions, including Hinduism, Buddhism and Jainism.
Appropriation and following complete perversion of the original symbolic meaning does not make the resulting output interchangeable with the original symbol.
Even Hitler himself in his book Mein Kampf states;
> "I myself, meanwhile, after innumerable attempts, had laid down a final form; a flag with a red background, a white disk, and a black hooked cross in the middle. After long trials I also found a definite proportion between the size of the flag and the size of the white disk, as well as the shape and thickness of the hooked cross."
Nowhere, ever, was the Swastika and its symbolic meaning mentioned as a direct inspiration for the Hakenkreuz. Instead, the Nazis attributed their own ideology to the symbol, but not even to the Swastika itself, but to its form, and furthermore that doesn't change anything about the Swastika itself.
It is not the same symbol.
If we're going to argue about the visual aspect of the symbol, please look at this image and tell me if these two symbols look like the same to you.
You're cherry-picking, poorly, from the Wikipedia article.
How does your selected sentence help your point?
> The swastika symbol, 卐 or 卍, is an ancient religious symbol in various Eurasian cultures, now also widely recognized for its appropriation by the Nazi Party
Also you tried to pick the two visual representations that are the most different, but the first image in the article[1] has the subtitle "The swastika is a symbol with many styles and meanings and can be found in many cultures."
The second image's subtitle says "The adoption of the swastika by the Nazis and neo-Nazis is the most recognisable modern use of the symbol in the Western world."
The symbol is the same symbol.
One is just "what the Nazis called that symbol".
The other is "what everyone else calls that symbol".
https://en.wikipedia.org/wiki/Swastika
Also translation is not an exact science where the most literal translation like "hooked cross" wins. It's much more often about conveying the meaning to the audience (who all correctly call that symbol a swastika).