I have found a solution to my problem. If I change the name of the variable to "offset" it runs correctly. Note that this is without the brackets that are used in the documentation example. As if I leave it as "{offset}" it tries to call the api as "{1}". I have no idea why it substitutes "{page}" to "1" in the setup used in the question, nor why it substitutes "{offset}" to "{1}".
At the end, this is how my source looked:
And this is how the copy activity source tab looked: