Style: Decide between `foo.rs` and `foo/mod.rs`

Problem you are trying to solve

It's time to decide between foo.rs and foo/mod.rs. (I'm slightly inclined towards foo.rs.)
by @rami3l in https://github.com/rust-lang/rustup/pull/3882#issue-2356320731

I still find [foo.rs imposing] non-trivial cognitive overhead because it means each module appears twice in the directory tree, and I have to decide which one I need to open.
by @djc in https://github.com/rust-lang/rustup/pull/3882#issuecomment-2172312913

Happy for us to have a discussion then about what style the project should take, but I've found the opposite - foo.rs means the module file path is always the same, whether or not the module has child modules, or is a leaf itself where a directory with just the module file would be tedious.
by @rbtcollins in https://github.com/rust-lang/rustup/pull/3764#issuecomment-2048428811

Solution you'd like

Unify the style of source file organization across the codebase to either one of them, completely eliminating the trace of the other.

Notes

No response

Start by reviewing the existing source tree to identify both module-file styles, then read the discussion in PR 3882 and the linked PR 3764 for the competing trade-offs. The related PR 3889 is also relevant context. Done means the project has one consistently applied source-file organization style with no remaining use of the other.