But the Norwegian government has absolutely nothing to do with who gets the prize, which is the whole point here. The fact that China gets angry at Norway et al because of a committee in Norway gave the peace prize to someone almost nobody in China knows about is a bit petty.
The cabinet doesn't directly award the prize, no. But Parliament chooses the people who choose the prize. That seems like exercising a pretty strong degree of control over who gets the prize, as with any other committee appointed by Parliament. And worse, they are specifically political appointments, not an attempt at appointing a quasi-independent "body of experts". There was a move some decades ago to change the makeup so the committee would be comprised of independent experts, from e.g. the academic, NGO, or scientific sectors, and maybe even including non-Norwegians. But that was rejected, so the committee continues to be staffed exclusively by important politicians.
For example, the current committee has the following members: Thorbjørn Jagland (Labour Party), Kaci Kullmann Five (Conservatives), Inger-Marie Ytterhorn (Progress Party), Berit Reiss-Andersen (Labour Party), Gunnar Stålsett (Centre Party).
A slightly different way of putting it might be: the Nobel Prize is awarded jointly by the major political parties of Norway, via their chosen representatives.