There are many reasons why English is the lingua franca today. It’s widespread around the world. The British Empire was pretty effective at spreading it till the middle of the 20th century, making it official language for a huge part of the world population. Since the fall of the empire an other English speaking country, the US has been carrying the flag with even more energy, spreading it even further with business, culture, hard and soft power. It’s a nice addition that English is a very easy language to learn for half of the world, definitely way easier than some other languages that previously rivaled English.
When we are looking at Mandarin it lacks just pretty much all the above drivers to become a global lingua franca. It’s limited to a very small number of countries that are all in Asia. It’s known language virtually only by ethnic Chinese people on other continents. Nobody else.
China itself isn’t a monolingual country either. While it’s the most spoken language but Mandarin actually is the lingua franca of the country.
Chinese is a famously tough language to learn. Not only the writing but also the tonality and the seemingly endless number of words that sound identical for the untrained ear.
While the Chinese economic power is very strong, the soft power isn’t exactly robust. Exceptionally rare to see anything from the Chinese popular culture to gain any attention globally. Can’t compete not only the American but even the British as far as global reach is concerned. And this doesn’t help the popularity of the language either