Rollup merge of #136161 - notriddle:typescript, r=GuillaumeGomez

rustdoc: add nobuild typescript checking to our JS

By nobuild, I mean that the type annotations are all [in comments], not in the "native" typescript syntax. This is a bit uglier, but it lets you rapid-prototype without tsc, works with all the native browser debugging tools, and keeps Node out of Rust's bootstrap chain.

[in comments]: https://news.ycombinator.com/item?id=35892250

This pull request mostly just adds ts-ignore annotations and type declarations. To actually take good advantage of typescript, we'll want to "burn down" this pile of unsafe code until we eventually have a version with almost none of these.

This PR also adds tsc to the mingw-check Dockerfile, so that it can't fall out of date like the Closure annotations did.

https://rust-lang.zulipchat.com/#narrow/channel/266220-t-rustdoc/topic/typescript

r? `@GuillaumeGomez` `@lolbinarycat`

Author: fmease