One thing you might miss in TS is the ability to just try to check or cast an object at run-time to check that it's really of some nominal type, or structurally compatible with some type/interface. TS can't do that because it doesn't have runtime type information for its types - the types are a compile-time only thing. TS does allow creating functions that return type predicates, but that requires your own manual checking as implementation, the type system can't help you write those as far as I know.
I was missing this mostly for incoming requests. A good solution for me has been to generate json-schema from typescript interface definitions, using the typescript-json-schema npm package. Then incoming data can be checked vs the generated json schemas. Works fine and I get json schemas for api endpoints from it as well, so no complaints.
It's a bit more complicated than that because of JS's prototype-oriented object system. If MyCustomType is a proper prototype (say you built it with the class keyword) you can certainly instanceof it. (That said there are strange edge cases where statically typed class-based object intuition falls down against prototype-oriented reality.)
The issues tend to start cropping up as you get further into TS-specific types like generic types. In a statically typed language you can inquire about the specifics of an implementation of a generic directly, and often even dispatch directly on that type. JS has no concept of your generic wrapper type and you need some other flag or logic to determine the runtime type of your generic code.
But in TS itself structural typing is used everywhere for actual type checking (except for classes with private members), and from my understanding there's no way to have TS help you check at runtime whether a type is structurally compatible with a value.
I was missing this mostly for incoming requests. A good solution for me has been to generate json-schema from typescript interface definitions, using the typescript-json-schema npm package. Then incoming data can be checked vs the generated json schemas. Works fine and I get json schemas for api endpoints from it as well, so no complaints.