Auto merge of #125145 - Kobzol:ci-toolstate, r=Mark-Simulacrum

CI: fix toolstate publishing

Toolstate publishing after something broke was not working (discovered [here](rust-lang/rust#124050 (comment))). The toolstate env. vars should only be needed for the publishing step, so I moved them there.

The toolstate script is also being checked in `mingw-check` on PR and auto CI, but it doesn't really seem to do anything, and it shouldn't require the token.