[erwinzhang7]

Related to #3442.

init(backend="any") tries backends in order and takes the first that initializes. Open MPI
initializes successfully for a program that was not started with mpirun, giving an
MPI_COMM_WORLD of size 1. That counted as success, so the chain stopped at mpi and never
reached the backends after it. A correctly configured JACCL job would then run single node and
report nothing.

mpi::init now returns nullptr when the world holds a single process, so any carries on to
the next backend. Asking for it directly with backend="mpi" and strict=true raises instead:

[mpi] The world has a single process. Launch with mpirun to initialize the mpi backend.

The size comes from mpi().world() rather than from a constructed MPIGroup, because building
one and discarding it runs ~MPIGroup(), which calls finalize_safe() when global_ is set,
and MPI_Init cannot be called again after that.

The second hunk is needed to make the first safe. register_group only caches under "any" for
a non-null group, so once mpi::init can decline, nothing is cached and the next init() call
re-runs the whole chain. init_safe() called MPI_Init unconditionally, and Open MPI treats a
second MPI_Init as fatal:

Open MPI has detected that this process has attempted to initialize
MPI (via MPI_INIT or MPI_INIT_THREAD) more than once.  This is erroneous.
*** MPI_ERRORS_ARE_FATAL

That is unreachable on main today, because a successful mpi group is cached and init_safe never
runs twice. init_safe is idempotent now.

Verified

Open MPI 5.0.9, macOS 26.6.

case	result
libmpi present, no mpirun, init()	mpi not selected
libmpi present, no mpirun, init(strict=true)	[distributed] Couldn't initialize any backend
libmpi present, init(backend="mpi", strict=true)	raises the message above
libmpi present, init() twice	no crash
mpirun -n 2, init()	size 2, ranks 0 and 1
mpirun -n 2, init(backend="mpi", strict=true)	size 2, no raise
mpirun -n 2, all_sum	[3.0, 3.0, 3.0, 3.0]

The first two rows match running with MLX_MPI_LIBNAME pointed at a missing file, which is the
intent: with Open MPI installed but no mpirun, MLX behaves as though it were not there.

[angeloskath]

I don't think that this is the correct fix. I would instead only return successful MPI initialization if the world size is larger than 1.

[erwinzhang7]

Reworked: mpi::init now returns nullptr when the
world has a single process, and the warning is gone.

One thing falls out of it. Returning nullptr there made a latent crash reachable:
register_group only caches under "any" for a non-null group, so nothing is cached, the next
init() re-runs the chain, and init_safe() called MPI_Init a second time, which Open MPI
treats as fatal. init_safe() is idempotent now, which is the second hunk.

Checked with Open MPI 5.0.9: without mpirun, init() no longer selects mpi and behaves the
same as with libmpi absent; init(backend="mpi", strict=True) raises; under mpirun -n 2,
init() still gives size 2 and all_sum is correct.

Fixed.