You say "even" as if it's a conservative estimate, but to me 50% of the country's population being infected by the same virus sounds extreme. Wouldn't this be on the extreme side?
If we assume that this virus is as infectious as the common cold, we can expect the infection rate within a household to be approximately 25% of contacts. That means that of the people you LIVE with, 25% will catch it from you.
50% infection rate in a large, distributed population like China would be very extreme.
Those colds that you’re seeing represent common symptoms of many viruses (metapneumovirus, paraflu, influenza, rhinovirus, RSV, etc, etc ... and many of these have multiple subtypes which can be concurrently circulating). In other words, you’re noticing common symptoms not necessarily the same virus.
Peak cold symptoms last about 3 days. I never said 50% of the population have the same cold at once. 50% catching it over a 6 month period is very reasonable.