How many different nations in the world have a state immunity act, or something equivalent?
You will likely need to compile this information. You can start with consulting a handbook like Anthony Aust's Handbook of International Law, which contains a chapter on state immunity laws.
You could also try to get your hands on The Law of State Immunity which provides an overview of the topic and likely references for looking further. You should be able to request both books through interlibary loan service at your local library.
The state immunity controversy in international law private suits against sovereign states in domestic courts
by Ernest K Bankas
has a list but you will need to update it. It might be a good place to start.
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