Auto merge of #141657 - petrochenkov:nobinroot, r=jieyouxu

bootstrap: Remove `bin_root` from `PATH`

It's not currently load bearing in typical setups on typical targets.
Basically, if it passes the standard CI, then we can remove it, I think.

If someone later reports this breaking the build, then we can address it in a more fine grained way.
E.g. add it to `PATH` last and not first, only on specific targets, and only if specific files are not already found in `PATH` directories.

Fixes [#t-infra/bootstrap > Build broken in MSYS2 @ 💬](https://rust-lang.zulipchat.com/#narrow/channel/326414-t-infra.2Fbootstrap/topic/Build.20broken.20in.20MSYS2/near/520709527)

Author: bors