Good morning, Olegv.
(1) I believe you are quite correct: "what" in your sentence is a so-called
indefinite relative pronoun:
The act in what ( = that which) is set to be a protracted legal battle. =
The act in that (which is set to be a protracted ....). "Which ...battle" is
an adjective clause modifying "that."
(2) Here are some other examples from my favorite grammar book:
That is WHAT (that which) I said before. = That is that (which I said before).
Do WHAT (that which) is right. = Do that (which is right).
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