Most languages don’t do type inference in “signatures” (function, but also class/struct members), as it would give you negligible benefit, a huge cost for the compiler and is commonly thought of as a bad practice.

Out of Scala, Rust, I believe even Kotlin, none do inference in these places. Even Haskell, which does infer function signatures as well, need explicit type annotation for `data` definitions.

typescript does such inference.

I disagree with you about huge cost for the compiler and benefits are the same as in normal code block: reducing boilerplate.

Typescript’s type system is deliberately not sound though.

In general, there is no type inference available for OOP type-hierarchies as opposed to a more Haskell-like type system, where Hindley-Milner works

I don't have strong knowledge in types theory, but why

class C { a: int = 0; }

can't be replaced with

class C { a = 0; }

? what issues it brings?..

That can. But what about a field that is not initialized there?

obviously you would need to provide type.