Obligatory reminder that policies can change very fast and without notice, especially in China where one case can send a city into lockdown mode. The upcoming Chinese new year may lead to stricter measures.
Also, do not rely on online information too much, especially if it is more than a week old. You really have to (or ask your family, friends, sponsors to) call the local neighbourhood community health officials, "health command" or the residents' committee to confirm current policy, unless you are going to a more administratively advanced city, e.g. Shanghai.
Various Chinese provinces and cities implement strict policies that include 14-28 days of facility quarantine (e.g. at a designated, quarantine-only hotel), followed by self-isolation at home and other public health measures. They are commonly referred to by a "numeric label" in the format of "X+Y(+Z)", X is the number of days of facility quarantine, Y and Z for other type of restrictions.
Costs are usually not covered by government; the costs per day are usually reasonable for the market but above average (you still have to pay for 14-28 days though). But the conditions and rules of the facilities differ a lot, e.g. some are super clean, some are not so clean, some would allow you to receive food and other merchandises you bought online, some force you to pay for overpriced food they offer.
During quarantine and isolation, you will have to undergo multiple PCR tests (sampled from your nose!); some places cover the costs of testing or make them eligible for insurance coverage.
Note that Chinese policies may differ not only based on your port of entry, but also on your place of residence and, for Chinese citizens, also the registration place of your Hukou (for foreigners, the place of business of your sponsor might also count), depending on the local rules.
The least strict policy I know is in Shanghai, where a "14+7" policy is adopted, at least for people with official/registered Shanghai place of residence. After 14 days of hotel quarantine, there is a 7-day period of health monitoring during which you are only allowed to go out for essential reasons, with masks, and must avoid crowded areas. In total, at least 6 and up to 8 PCR tests will be carried out.
The most strict I know of currently, Shenyang in Liaoning province has recently adopted a "28+28" policy, with 28 days of facility quarantine, followed by 28 days of health monitoring during which period you are not allowed to leave the city without government's consent and must follow instructions given by your neighbourhood health officials. 6 PCR tests and two blood tests will be carried out during the facility quarantine and two tests are required during the health monitoring period.
During the recent outbreak in Heilongjiang, "21+14" was adopted with 14 days of self-isolation at home. But there may have been a relaxation recently (not confirmed).
If you enter from Shanghai and after your facility quarantine there ends, you will still need to quarantine the rest of required days at a hotel when you arrive in e.g. Shenyang. But if you qualify for the health monitoring programs in Shanghai or nearby regions (e.g. with an eligible registered address), you can be treated as a domestic arrival after e.g. 28 days (depending on the rules at your destination) after entry into China.