Reorganize `Process` to include extra global states

This was part of the original plan after #3803, but we probably have put it aside for a while:

In https://github.com/rust-lang/rustup/pull/4182#issuecomment-2663126604, I've noticed that the current Process abstraction should probably be extended to allow the existence of a tracing_subscriber global state, so that we can handle graceful shutdown more easily.

Having noticed the clear pattern here:

https://github.com/rust-lang/rustup/blob/52e6070c98ca8f4c26fce9107ff8310323dfa700/src/bin/rustup-init.rs#L44-L53

... it should probably be modeled as an RAII guard.

I have also noticed that this should resolve another problem, i.e. the corresponding construct in tests is simply no longer used, as these two functions no longer have a caller:

https://github.com/rust-lang/rustup/blob/52e6070c98ca8f4c26fce9107ff8310323dfa700/src/test.rs#L235-L250

This is most probably caused by the removal of rustup_macros (https://github.com/rust-lang/rustup/pull/3877/commits/d60f0058503954f57786d16e15a2d42f6798e141): indeed, the tests are passing on the CI, but sometimes one might want to run tests with otel on as well.

@djc What do you think?

Read src/bin/rustup-init.rs around the existing global-state setup and src/test.rs around the unused test functions. Review the discussion in #3803 and pull request #4182 before deciding how Process should represent the tracing_subscriber state. Done means the RAII-based organization supports graceful shutdown and tests can still run with otel enabled.