You wrote it correctly. People in the U.S. Would Say "It's hard to estimate how much activity was lost".

Great question. How much economic activity is . . . is talking about the action or work. It is like saying 'How much economic action is . . . ' How many economic activities are . . . is talking about the groups or organizations of recreation. It is like saying 'How many economic sports are . . . '

There are two different main uses of "activity", and no, they cannot be interchanged like that. Both of those sentences are grammatically correct, but they do not have the same meaning. If "activity" can be pluralized, then it goes with "many". This version of "activity" is something akin to "quantified object that can be experienced or acted upon". For instance, you can have a list of homework activities, or many activities at the YMCA, or a list of activities you like to do in your spare time (aka hobbies). If "activity" cannot be pluralized, then it has become a main noun with a noun adjunct. The other noun modifies and defines it as though that other noun were an adjective, and this version of "activity" essentially means "to be active, moving, or productive". For instance, a team of geologists may be tracking earthquake activity on a fault line. The activity they're looking for is the quaking activity of the earth. "How many activities do you have at the YMCA?" "Oh, we have nearly forty separate activities!" "How much earthquake activity was there this week?" "It was only a 3.3 on the Richter Scale." These are both correct conversations. However, switching the type of "activity" changes one entirely and makes the other gibberish. Observe: "How much activity do you have at the YMCA?" "People come in for most of the day until closing, but 3-5 PM is the worst, and it's almost dead past 9 PM." <------------As you can see, the responder is now talking about how active the PLACE was instead of talking about what "activities" one could experience there. "How many earthquake activities were there this week?" "What are you talking about, Steve? Do you mean to ask me how MUCH earthquake ACTIVITY there was?"

I think using how much is correct.