`rustup override set nightly` cannot be seen in `rustup toolchain list`

[bestia-dev]

rustup override set nightly overrides the default toolchain for that directory only.
But in rustup toolchain list this cannot be seen. There is only the old default:

stable-x86_64-unknown-linux-gnu (default)   
nightly-x86_64-unknown-linux-gnu  

It would be informative to add something like (override):

stable-x86_64-unknown-linux-gnu (default)   
nightly-x86_64-unknown-linux-gnu  (override)

[kinnison]

This is an interesting idea and should not be too hard to implement. If you wanted to have a go at a PR, I'd be happy to discuss things with you. You can find me on our Discord channel on the rust-lang server. If you (or anyone else reading this) wants to take this on, comment on here so we know and don't duplicate work.