The last example is surprising:

  {
    await using { connection } = getConnection();
    // Do stuff with connection
  }   // Automatically closed!

The object returned by getConnection() is destructured to extract the field named connection and assign it to a local variable with the same name. The containing object presumably continues to exist anonymously so its Symbol.asyncDispose function will still be called when it goes out of scope.

Can anyone explain which language rule guarantees this behavior in C# and in TypeScript?

I'm pretty sure that example won't work and is based on an old version.

But assuming a javascript implementation where it works, I don't know what you mean by "language rule". The spec says what "using" means, and it doesn't require any behavior the language doesn't already have. The old spec said "When try using is parsed with an Expression, an implicit block-scoped binding is created for the result of the expression.", and the new one says "When a using declaration is parsed with BindingIdentifier Initializer, the bindings created in the declaration are tracked for disposal at the end of the containing Block or Module". Then the spec has an example implementation written in javascript, with the value being added to a (non-user-accessible) list. https://github.com/tc39/proposal-explicit-resource-managemen...

Is that the language rule you wanted?