Migration of `lightning.gpu` device to the new device API

[LuisAlfredoNu]

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Context: Following the design of Lightning Qubit and Lightning Kokkos that use the New Device API, we can now migrate Lightning GPU device to the new device API.

Description of the Change: Migration of Lightning GPU with MPI support to integrate the New device API. The list of main feature changes are

• Add the MPIHandler state_vector, measurements, and adjoint-jacobian classes for lightning.gpu.
• Add the simulate, jacobian, simulate_and_jacobian, vjp, and simulate_and_vjp methods to lighting.gpu.
• Add MPI support to lightning.gpu with the New device API.
• Update unit/integration tests for the new device API to work with lightning.gpu
• Check the full support for sampling in full parity with Lightning Qubit
• Replace the old device API for Lightning GPU.

Benefits: Full integration of Lightning GPU with the new device API.

Possible Drawbacks:

Related GitHub Issues:

[sc-70964] [sc-59219]

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 95.92199% with 23 lines in your changes missing coverage. Please review.

Project coverage is 96.97%. Comparing base (3e9b4be) to head (8659b2e). Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
pennylane_lightning/lightning_gpu/_measurements.py	94.04%	5 Missing :warning:
pennylane_lightning/lightning_gpu/_state_vector.py	95.61%	5 Missing :warning:
pennylane_lightning/lightning_gpu/lightning_gpu.py	96.66%	5 Missing :warning:
pennylane_lightning/core/_measurements_base.py	85.71%	2 Missing :warning:
pennylane_lightning/lightning_gpu/_mpi_handler.py	95.65%	2 Missing :warning:
...nylane_lightning/lightning_kokkos/_state_vector.py	66.66%	2 Missing :warning:
...ylane_lightning/lightning_gpu/_adjoint_jacobian.py	98.85%	1 Missing :warning:
...ane_lightning/lightning_kokkos/lightning_kokkos.py	80.00%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #853 +/- ## ========================================== - Coverage 97.18% 96.97% -0.21% ========================================== Files 211 132 -79 Lines 29198 17041 -12157 ========================================== - Hits 28376 16526 -11850 + Misses 822 515 -307 ```

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[github-actions[bot]]

Hello. You may have forgotten to update the changelog! Please edit .github/CHANGELOG.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
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[multiphaseCFD]

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