I agree; but I _think_ chronologically Node & server-side-JS came first? The driver is the same though: "larger codebases, running on top of Javascript" - and indeed nowadays probably the browsers are the things that run the larger codebases.
Typescript evolved from an internal project at Microsoft where they were trying to do their own GWT, but with .NET instead of Java, the browser was definitly first.
Just like VSCode started as the Web IDE Monaco, written in this new Typescript thingie, before pivoting into Electron.
I would dare to say that more people use Typescript in frontend than in backend projects, so basically Typescript killer "app" is the browser, because you are forced to use Javascript, but JS does not scale that good for mid, big projects.