This thread has gone in an...odd direction. FWIW, I'm a medical researcher whose research includes evolution of the immune system and some microbiota stuff, so this is somewhat my "wheelhouse".
For the record, evolution is formally defined as "the change in the heritable characteristics of biological populations over successive generations", which means that changes in gene frequency (e.g. selection) over a single generation are, indeed, evolution. As are bigger physiological changes taking place over eons. There is no "line" below or above which change isn't evolution - if gene frequencies change, or a new mutation is introduced, or an existing gene variant eliminated, or a new species formed, its all evolution.
We could speculate that all organs are under positive selection so long as that organ does something necessary to survival. Now explain why humans have an appendix. Before you get too far with this, recall that we all have an appendix and it has been retained for millenia. It is doing something!
The appendix has not been retained for millenia; its been continually shrinking for several million years, and a small portion of humans are born completely without one. The appendix has a very well understood job in other closely related primates, which is the "culture" of cellulose-digesting bacteria to aid in the consumption of woody plants. We have not needed this feature for ~4 million years, and have experienced a concordant reduction in the size of our appendix. Whether the residual appendix has a function in humans is unclear, but most of the data is consistent with it being vestigial - most of the proposed purposes (immune site, culture of other microbiota components) have not stood up to scrutiny.
You're also making a common mistake in your thinking of evolution - you are assuming that something without a function will be eliminated. This is often not the case - selection is in constant competition with other evolutionary forces such as genetic drift, which tends to retain features. To be eliminated, a "useless" feature must carry a survival cost (e.g. be harmful) that incures a selective force greater than the "equalising" force of drift. Meaning, if there is no meaningful evolutionary cost to keeping a useless trait, that trait will tend to persist, with whatever change that occurs, occuring slowly and without direction.
Here's a humbling thought - drift, not selection, is the major evolutionary force that separated us from chimps. Only about 5% of our genes - and mostly immune system genes at that - show evidence of selection.
The appendix occupies the same area as the float bladder in fish. What it does today was only sussed out a few years ago. Basically, it stores microbiota that reboot the gut in the event of some types of illness. We can live just fine without it in the modern world, but would often have needed it in the past.
None of this is correct. Appendices have evolved over 30 times in vertebrates, usually out of the need to generate a "fermenter" to breakdown difficult to digest foods. The appendix evolves as an outpocket as the gut - which is also where swim bladders and lungs come from - which may be where your confusion comes from. It did not evolve from the swim bladder - our lungs evolved from
swim bladders. The idea that the appendix acts as a reservoir for our microbiotia was never more than supposition, based on the observation of biofilms in it. There isn't really any data beyond that to support that idea - in fact, people without an appendix appear to have a more stable microbiota than those without one.