IMO it's better to just use TypeScript anywhere that you'd normally use Perl. The type safety helps later on when you revisit old code plus I think it's more productive overall, having used Perl many times in the past.
Nooooo. Python's the clearest front-runner in the Perl replacement game. I wish it were Ruby, but it's pretty clearly Python. TS changes too fast and requires too many tools, it's not even a serious contender in this category, though I much prefer it to any of the above for large programs.
Python has some semi-decent type hinting, these days. It's not so bad, it'll keep you out of most of the same trouble that TypeScript does.
Typescript is a great remedy when you are forced to use JavaScript. But in a context where you can use any language it makes zero sense. If you want static types just use C# or whatever, otherwise just use Python.
While I see benefits of TypeScript's type system, I think the lack of a special compilation step is a big win for Perl, at least in the author's eyes. (Yes, I know Deno is a thing, but I'm not sure of the extent which the author considered it).
You can run ts-node to execute TypeScript to run it without having to manually compile it first. Although if you have a large TypeScript program with a lot of dependencies or on an older machine, I guess it could take some time. With my own scripts I've only seen it take a few seconds at most.