In the Android debugger window, a SearchView has many fields, some of which are depicted below.
Which field shows the current query text of the SearchView?
If the fields are not sufficient for displaying the information you need, you can use the Evaluate Expression as depicted in the first answer to the linked question.
As pointed out by @ShivamKumar, typing in searchView.getQuery()
at any break point where the stack still has direct access to searchView will give you what you want.