You need to explicitly tell TypeScript the type of the HTMLElement which is your target.
The way to do it is using a generic type to cast it to a proper type:
this.countUpdate.emit((<HTMLTextAreaElement>e.target).value./*...*/)
or (as you like)
this.countUpdate.emit((e.target as HTMLTextAreaElement).value./*...*/)
or (again, matter of preference)
const target = e.target as HTMLTextAreaElement;
this.countUpdate.emit(target.value./*...*/)
This will let TypeScript know that the element is a textarea and it will know of the value property.
The same could be done with any kind of HTML element, whenever you give TypeScript a bit more information about their types it pays you back with proper hints and of course less errors.
To make it easier for the future you might want to directly define an event with the type of its target:
// create a new type HTMLElementEvent that has a target of type you pass
// type T must be a HTMLElement (e.g. HTMLTextAreaElement extends HTMLElement)
type HTMLElementEvent<T extends HTMLElement> = Event & {
target: T;
// probably you might want to add the currentTarget as well
// currentTarget: T;
}
// use it instead of Event
let e: HTMLElementEvent<HTMLTextAreaElement>;
console.log(e.target.value);
// or in the context of the given example
emitWordCount(e: HTMLElementEvent<HTMLTextAreaElement>) {
this.countUpdate.emit(e.target.value);
}