If that last category doesn't succeed that doesn't mean the test flight was a "failure" from the businesses perspective. They still got what they wanted, they just didn't get the icing on top.
The test flight that destroyed the pad is properly categorized as a failure. The flight termination system was expected to work. They expected not to cause that much damage to their infrastructure and surroundings, their relationship with the FAA, their ability to get licenses, etc. To argue that it wasn't a failure, you have to argue that the flight termination system was in the category of systems where a failure was considered acceptable. If that was the case, everyone involved in launching that flight ought to to go jail for recklessly endangering the public.
The most recent test flight though seems to have been a pretty resounding success. Everything that they said they really wanted to see happen, happened. Yes, both stages had failures in "we might not even get here" test objectives after that. That's ok.
Demonstrably incorrect.
Examples:
https://www.youtube.com/watch?v=AqeJzItldSQ is a Saturn launch abort test that failed. It failed in a way that they were able to determine that intended test would have worked, though. 1:20 for the meat of things.
https://en.wikipedia.org/wiki/Apollo_6 also failed to achieve its objectives; "Despite the engine failures, the flight provided NASA with enough confidence to use the Saturn V for crewed launches; a potential third uncrewed flight was cancelled."
All that aside, SpaceX was quite clear that the latest Starship test had multiple objectives, and that "successfully splashdown near Hawaii" was deemed quite unlikely. It successfully demonstrated a number of items, including fairly critically the launchpad changes. It wasn't one test; it was a bunch of tests in one flight.