> there's no accepted definition of what an unsound type system is
Huh?
The cheeky answer would be that the definition here is the one the TypeScript documentation itself uses[1].
The useful answer is that there’s only one general definition that I’ve ever encountered: a type system is sound if no well-typed program encounters type errors during its execution. Importantly, that’s not a statement about the (static) type system in isolation: it’s tied to the language’s dynamic semantics.
The tricky part, of course, is defining “type error”. In theoretical contexts, it’s common to just not define any evaluation rules at all for outwardly ill-typed things (negating a list, say), thus the common phrasing that no well-typed program must get stuck (unable to evaluate further). In practical statically-typed languages, there are on occasion cases that are defined not to be type errors essentially by fiat, such as null pointer accesses in Java, or escape hatches, such as unsafeCoerce in practical implementations of Haskell.
Of course, ECMAScript just defines behaviour for everything (except violating invariants in proxy handlers, in which case, lol, good luck), so arguably every static type system for it is sound, even one that allows var foo: string = 42. Obviously that’s not a helpful point of view. I think it’s reasonable to say that whatever we count as erroneous situations must at the very least include all occurrences of ReferenceError and TypeError.
TypeScript prevents most of them, which is good enough for its linting use case, when the worst possible result is that a buggy program crashes. It would definitely not be good enough for Closure Compiler’s minification use case, when the worst possible result is that a correct program gets silently miscompiled (misminified?).
[1] https://www.typescriptlang.org/docs/handbook/type-compatibil...