Is it legal to mandate Covid vaccines?

This is a loaded question, because it implies it is a matter of legality, instead of a matter of ethics.

I think it is not ethical to mandate it, because that is essentially forcing people to trust the authorities and scientists. People don't have a rational reason to trust these entities.

So it is quite obvious that it is unethical and a violation of basic human rights.

It is up to each government if they want to protect the basic human rights of their citizens, and do things that can gain the trust of the people, or just apply brute force in a time their population is vulnerable and might give up their basic rights in return for the promise of improved protection from disease.