Not really. They are a mixed economy with a declining public sector. The Iron Rice Bowl (guaranteed life employment and distribution of social welfare via industry) is virtually a thing of the past. Socialism - real socialism - involves control of key industries (check) by the proletariat (nope). Their economic system is more oligarchal capitalism than it is 'socialism with Chinese characteristics', as they like to call it.
They have an entrenched single-party state propped up by the military and a handful of corporations (most of which are from overseas, but that's beside the point). The only divergence from the classical fascist model is the lack of a current personality cult (Mao had one, but his government wasn't fascist). Even so, there have been fascist governments in the past where there either a personality cult (Hungary being one example).
Xi has a massive personality cult.
Mao is the greatest murderer in human history. Who cares if he is labelled facist or not given his murder count.