I wouldn't go as far as to say that as it implies fascism to be a direct successor to syndicalism and that is more than misleading.
Fascio was literally the Italian word for "trade union" at the time.
Fascism didn't branch off directly from any core socialist though, but rather was made from a weird hodgepodge of socialist ideologies that were the most popular to the masses. (Such as healthcare, social welfare, anti-smoking, anti-gun, ect.) They then discarded the remnants that weren't broadly popular (Open state enforced atheism, the abolition of private property, complete social redistribution through collectivization, ect) .
If we can look at how they historically acted, fascist groups in power
did do things like
de facto eliminate private property and collectivise agriculture. This is entirely logical since, as I said, fascism is a form of socialism. We even see the exact same Marxian myth that the totalitarian government will wither away once Da Revuhlooshun is complete. But fascism is, well, more honest about the
means of its political program (which is evil and stupid regardless of said means) than most socialists go into. You won't find a single doctrine, policy or action of the NSDAP, for instance, that was outside of the socialist mainstream during the late 19th and early 20th centuries.
and adopted a pseudo, pretend to give a damn concerning traditionalism, religion and industrialism through capitalism.
Fascism is literally socialism in disguise, bar a few tenants, it tries to creep into your bed pretending to be on your side, when in actuality is doesn't give a hell about you or anything you stand for.
Heh, one of the big Italian groups that eventually helped to make up the fascist party was literally called "the futurists".
I think one of the reasons the socialist nature of fascism isn't understood is that there were no fascist "revolutions" to speak of - fascist groups never had the strength to take power by main force (ironic given their obsession with the "purity" of violence, which they got together with the Bolsheviks from Sorel and the anarchists that plagued the late 19th century) and instead tricked weak conservative establishments into handing them the reins by making appeals to tradition and religion (which were all lies). There was no opportunity to start straight over with a relatively clean slate and hence purely as a result of the way they came into power and their relatively short lifespans they never got the chance to totally remake society into their nightmare vision of Real True Socialism. Just a different head of the hydra trying to swallow civilisation whole, in the end.
