> the most catastrophic outcome
Nah, this is in the context of C++ so UB isn't the most catastrophic situation. Undefined Behaviour is a behaviour, which means we might well be able to avoid invoking the behaviour and then it's fine. For example if your C++ program has a use-after-free in the code invoked only by the "Add file" feature but otherwise works fine, we can just ensure operators never use "Add file" and the UB, no matter what it might be, won't happen.
C++ has IFNDR, clauses which say this is "Ill-Formed, No Diagnostic Required". The program itself wasn't actually a valid C++ program, it has absolutely no defined meaning, there may be no indication of a problem from your compiler but alas it's entirely meaningless. This isn't behavioural, it's an invisible status of the entire program.
As I said, UB means that a program has no meaning in the source language. That doesn't change anything I wrote above about the impact of UB. A hardware fault may also make a program meaningless, BTW, yet we all accept that every program written in any language is currently susceptible to UB or to a hardware fault.
If you want, you can think of UB like a mathematical singularity in some physical theory. The theory of the language has nothing to say about what happens in such a program. But that doesn't mean that we can't reasonably talk about what happens not using that theory [1]. Indeed, one of the reasons that UB are of concern is that some of them are frequent causes of security exploits - and that's the thing we ultimately care about, not that the program loses its semantics. But again, not all of them are equally common causes of such outcomes, and not all of them are equally hard to avoid in the first place.
[1]: In fact, this is easy to explain in software: the programming language can say nothing about the meaning of a program with UB - indeed, it has no meaning in that language - but because we do have an executable, the program still has a well-defined meaning in the machine language it compiled to (machine language has no UB, or, even if some machine architecture does declare that some instruction stream is UB, most programs with UB in some programming language still do not compile to a program with UB in machine code). So the program that has no meaning in C++ still has meaning in machine code, and as that is the program we ultimately run and care about, we can talk about which UBs are more or less likely to result in which machine code behaviour.
This seems like it missed the point entirely?
UB is a behaviour, it's unbounded, so it's an immediate disaster, and "time travel" UB can make this harder to reason about, because the as-if rule can mean that although it didn't in some sense "happen" yet the behaviour has consequences earlier. But if we avert the behaviour it won't happen. It is not correct to say that UB means the entire program had no meaning.
You give the "mathematical singularity" analogy, consider division. We doubtless agree than 6 divided by 3 is 2. And 6 divided by 2 is 3. But how about 6 divided by 0? This is not defined, we cannot perform such an operation. But division is not as a result somehow entirely without meaning, it just has this well understood limitation. Likewise for software with UB that we can avert.
IFNDR is a catastrophe because it truly does render the entire software without meaning.
> IFNDR is a catastrophe because it truly does render the entire software without meaning.
In the language. I.e. the language assigns no meaning to source the program, which is, indeed, the "catastrophic" impact of UB (or IFNDR) within the theory of the language. But since a running program takes the form of an executable, and the executable always has a defined meaning in another language (machine code), while C++ has nothing to say about what such programs do (i.e. that's the end of the helpfulness of that theory) that doesn't mean we can't talk about or care about the meaning of the executable.
An executable that crashes and an executable that leaks all your secrets have very different consequences, and while the C++ spec says absolutely nothing about the relationship between different UBs and these behaviours, that doesn't mean that these relationships don't exist.
A mathematical singularity in a physical theory means that that particular theory has nothing to say about the physics of that situation, not that there's no actual physics going on, and the physics that is actually going on could be more or less "catastrophic" depending on what we mean by that.