Can Shaoxing social security card be used in Hangzhou?

Of course. However, it can only be connected to hospitals in Shaoxing, which are basically the largest county-level hospitals in the area. You need a social security card and a medical insurance book. The community township hospitals in Shaoxing can't use it. Now the whole province is connected to the internet. It can be used in the largest hospitals in counties and cities. However, the social security cards of some foreign personnel have not been replaced by CPU cards required by the provincial intranet (the original 4442 chip cards were issued by various places themselves), and they cannot be used in other places, including Hangzhou, and need to be replaced.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.