Do temporary residence permits have anything to do with social security?

At present, the basic old-age insurance is coordinated by the whole country, but it is settled by provinces. Generally, the insured person is required to manage it on the spot, that is, at the place where the household registration is located. But if you are in the same province, you can also participate in the insurance in the form of a temporary residence permit. The basic medical insurance is coordinated by all localities and is responsible for its own profits and losses, so it needs to be consistent with the place where the household registration is located, and the policies of all localities are not the same. I suggest you solve the hukou problem first and then apply for social security according to local rules.

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