Burner sims have been a thing of the past in China for quite some time. The official rationale I believe is to curb telecom fraud, which in turn left China and started doing their business in southeast Asia.
It's very easy to get. As a visitor, I got one in the airport for $20. "ID verification" is stretching it, but like so many things in China it requires the vendor to take a photo of your ID, and unusually also to take a photo of you and submit it to the telecom website.
This kind of SIM card worked fine for me to register for several online services in China earlier this year, including a Chinese ride sharing service and online shopping.
No, you don't need ID verification to use search engine or read news in China.
However, sites that depend on user-generated content (like forums) would ask for at least your phone number.