Yes, it is possible for governments to gain control of Bitcoin.
Several governments (US,China, Bulgaria…) are large holders of confiscated BTC.
In addition, in the case of China the largest and some smaller crypto-exchanges together with lots of BTC miners are located in the country.
As Bitcoin is a competitor of the China’s CBDC the country may take measures to control or manipulate BTC in order to get wider adoption of its CBDC.