What exactly does downgraded mean in this sense though? I assume it's just based on the government's/WHO's definitions, it doesn't mean that it isn't dangerous.

In the UK, a high consequence infectious disease (HCID) is defined according to the following criteria:

acute infectious disease
typically has a high case-fatality rate
may not have effective prophylaxis or treatment
often difficult to recognise and detect rapidly
ability to spread in the community and within healthcare settings
requires an enhanced individual, population and system response to ensure it is managed effectively, efficiently and safely
I assume to be high consequence the mortality rate would have to be over a certain percent. Even though covid isn't safe to have the mortality rate is still relatively low unless you are over 70.

Covid's danger seems to be more from how easily transmitted it is.