Why was Queen Elizabeth II dressed in black during her audience . . .?

Customary but optional garb for a Papal audience is black. However, certain Roman Catholic royal visitors-- The Queens of Belgium and Spain,and the Grand Duchess of Luxembourg--may wear white -- This is called "Privilège du blanc".

It's simply a custom, a tradition, whether you are Catholic or not. The late Princess of Wales did it, and so did Michelle Obama not so long ago. Neither of those women was Catholic.

It's also possible that at the time, the Queen was actually in mourning for someone. I don't know what year that photo was taken.

Protocol, and the Queen would wish to be a gracious guest and follow the optional dress code. Actually wearing white was something Roman Catholic monarchs did, so it is not surprising she did not wear white.

The Queen is not ROMAN Catholic but head of A catholic church herself so she was dressed with dignity, representing the Anglican Communion.

When meeting HH The Pope, you should wear white if you are a Catholic and black if you are not.