gh-112529: Use atomic operations for `gcstate->collecting` (#112533)

* gh-112529: Use atomic operations for `gcstate->collecting`

The `collecting` field in `GCState` is used to prevent overlapping garbage
collections within the same interpreter. This is updated to use atomic
operations in order to be thread-safe in `--disable-gil` builds.

The GC code is refactored a bit to support this. More of the logic is pushed
down to `gc_collect_main()` so that we can safely order the logic setting
`collecting`, the selection of the generation, and the invocation of callbacks
with respect to the atomic operations and the (future) stop-the-world pauses.

The change uses atomic operations for both `--disable-gil` and the default
build (with the GIL) to avoid extra `#ifdef` guards and ease the maintenance
burden.