chore: fix corepack wiring in integration tests (#10044)
### Description
Spun out from
https://github.com/vercel/turborepo/pull/10023#issuecomment-2679724673
setup_package_manager.sh exports `PATH`, so we need to source it for the
isolated corepack shims to actually get used in tests. Otherwise certain
npm integration tests can fail, depending on the global npm version and
if corepack's npm shims haven't been explicitly enabled globally. This
can lead to false positives and wasted time debugging integration tests
locally.
This hasn't been an issue under GitHub Actions, since actions/setup-node
is installing the same version of npm (10.5.0) that the tests expect,
but could otherwise become problematic down the road.
Fixing this uncovers two new problems around testing under Windows,
which this PR also addresses:
- the corepack path needs to be POSIX-ified, since
`C:\Users\RUNNER~1\...` contains backslashes and the name separator (:)
- corepack uses `PATHEXT` (via
[cmd-extension](https://www.npmjs.com/package/cmd-extension)) to
determine the casing of its shims' file extension (e.g. npm.cmd vs
npm.CMD), whereas node's bundled npm.cmd is always lowercase ... while
we could update all the tests to accept both styles, the easiest thing
to do is just to downcase `PATHEXT`.
### Testing Instructions
Integration tests 🥳
