Data is basically, two types, vector ( like shapefiles ) and raster. in the context of forests, vector data data are used for the various types of forest boundaries, administrative areas, ownership, easements, management zones, etc. Alternately, raster is used for the many various classifications schemes consisting of their particular types. These might be biological, structural ( like canopy cover ), ecological, species mix,, or even fire risk. And any organization or agency usually creates one specific to their own purposes - the USDA forest types by tree species ( ... Jack pine, Red pine, Eastern white pine, Eastern White pine / Eastern hemlock, Eastern hemlock, Balsam fir, White spruce ) https://data.fs.usda.gov/geodata/rastergateway/forest_type/conus_forest_type_metadata.php#5
One vector dataset of forest types in the USA are the jurisdictional boundaries of the USDA's Forest Service, The Bureau of Land management, Department of Energy, and the 50 different state level departments of natural resources and/or ecology. Then there are the various private and corporate forest land holdings. China is approximately the same area of the USA, so I would guess they have a similar hierarchy and types of administrative and management boundaries.
Similarly, the Chinese government agencies and departments probably have their own classification systems using different types for biological rasters.
There are also global datasets available that use classification systems that are uniform, at the loss of local detail.
A 'shape file of Chinese forest type' is analogous to asking for 'a picture of Chinese vehicles' - an airplane, a truck, a train? Made in China or just sitting in China? A single car or a city full of traffic? There are thousands if not tens of thousands of datasets, so being very specific will enable people to assist you better, especially describing what your hypothesis or research goal is.
Where have you looked so far, that you had difficulty, or determined that the data was insufficient for your purposes?
My guess is that there are hundreds of datasets related to forestry from NASA, ESA, and others, and derivative projects like https://glad.geog.umd.edu/ , you could look at the sources GLAD uses, for instance. NASA has raw data, processed data to certain levels, 'science ready' data in time series, targeted collections on various themes ( like GLAD ).
You could also maybe look at some of the 90,000+ papers about Chinese Forest Cover ( https://scholar.google.com/scholar?as_ylo=2017&q=china+forest+cover&hl=en&as_sdt=0,48 ). They always mention the source(s) of their data.
Another source might be https://data.globalforestwatch.org/ ... but be sure to read the documentation carefully. It is an collection / aggregation of many different sources and products, and may vary from country to country.