(Note however that while enjoy projects like these and also don't vilify most people who wrote JS-dependent websites, not even in my thoughts, I might think of those who write html with optional js-features as nicer people, more thoughtful/considerate and less childish ;-)
Using a typed languge is such a productivity boon.
The word productive on its own is wholly meaningless without elaboration. What makes a typed language productive? Does the size of the project matter?, why is vanilla js not productive? Is it a lines of code metric? Is it a test suite efficiency metric? Is it a quality metric?
But very briefly I would say that these are the benefits as I see it:
* Access to improved tooling. E.g. refactoring by renaming things is much easier to do without breaking things. Also auto-complete when using third party libraries is a huge benefit.
* Some errors are automatically caught during build-time. E.g. checking the data used in a template lines up with what the component should be passing to that template. Without typescript one should probably verify this via unit tests. With TS these tests are superfluous.
* Improved documentation. It's a lot easier to understand what the shapes are of data is that is being passed around in the application. It also provides the opportunity to define these in central locations (e.g. in the form of interfaces) which can then have additional documentation added to them.
I think the benefits are not so much specific to TS as they are general benefits of using types and a typed ecosystem.