Governments do test products now and then, yes. But they aren't in the habit of routinely testing new products when they hit the market. I don't know what prompted this particular test, but it wouldn't surprise me if the ANFR just one day decided to test a bunch of models of iPhone (or a bunch of phone models in general) kind of arbitrarily.

There was a similar case recently where Sweden's equivalent decided to test a bunch of models of EV chargers and found some lacking.

In general, outside of these random tests, "they check the paperwork, not the thing itself" is correct.

Sure, but the "accredited" in accredited laboratory is itself a paperwork audit-based process. This is how you get your own paperwork as a manufacturer to give to an auditor to say "Look at our paperwork". It doesn't mean the regulator is somehow testing things itself.