fix: use signal handler in shim (#4313)
### Description
I believe this fixes #3711
#4196 added graceful shutting down when calling `go-turbo`, this does
the same but for when we need to invoke the correct Rust binary in
`shim.rs`. I extracted the logic added in #4196 to a function that can
be used throughout the codebase.
### Testing Instructions
Currently only doing manual via the reproduction provided in #3711.
Edit: I originally wanted to add integration test to cover these cases,
this has proven to be a challenge. Will still look at trying to
orchestrate a test for this, but considering how much traction the
related issues have, I don't want to block on getting an integration
test.
