The real question I have is what does Italy really have to offer China? If it's a bridgehead into EU markets, there is already Hungary, Spain, Greece, Portugal, etc.
Similar to Germany and France, Italy's true trade value to China is advanced technology. To most casual observers, Italy is kinda like only exporting pasta, wine, supercars, fashion, luxury items, etc. But in the engineering and scientific fields, Italy is quite a major force, albeit lesser than Germany and France. Italy is also a major exporter of heavy machinery, defense technology, precision instruments, ships, and vehicles. China is the factory of the world, therefore Italian industrial firms are doing so much business there.
China is the favourite destination for Italian companies to sell their products and outsource their manufacturing. There are endless factories in China to sell your machinery to. And there are plenty of products that China can produce much more efficiently and competitively than the rest of the world. For instance, China is the #1 producer of electric motors, so it contract manufactures for plenty of European firms including Italian ones. China is also the #1 shipbuilder in the world, and Italian marine component suppliers are doing plenty of business in Chinese shipyards.
Also, Italy's academia is quite strong in STEM. They recruit lots of Asian assistant professors to do the hard work of crunching numbers for the local professors. I am quite sure that there are plenty of Chinese among them. They get to work in top Italian Universities and CERN, researching the cutting edge of science. Its a win-win deal. Italy gets from China, a quality labour force for their academia and research, while China get to create a talented pool of brilliant scientists to call home later. Things may still change, but Europe has so far not followed 100% with the US's madness of banning Chinese students from STEM research. For now, Europe should feel blessed that America is preferring Indian students over Chinese students, so more Chinese students for them.
That's just Italy. So we can imagine what kind of businesses Germany and France does with China. Europe has no true alternative to China. The US is not the factory of the world, its shipbuilding industry is pitiful, and their politicians are mafia, using long-arm jurisdiction to sabotage other businesses. Whereas India is just promises, hype, and noises.