Add lazy checkpoint loading for FSDP full-state checkpoints (Trainer)

[awaelchli]

What does this PR do?

Fixes #8043
Follows the same logic as added in #18150

Currently, loading a full checkpoint means replicating it in CPU memory for each process. This can cause CPU OOM on machines with limited CPU RAM. Instead, the approach of this PR is to lazy-load the checkpoint (no memory allocation) and on-the-fly load tensors as they are needed. This reduces the memory usage to only one weight tensor being stored in memory (per process) at a given time during model.load_state_dict() access.

cc @Borda @awaelchli @carmocca

[github-actions]

⚡ Required checks status: All passing 🟢

Groups summary

🟢 pytorch_lightning: Tests workflow

Check ID	Status
pl-cpu (macOS-11, lightning, 3.8, 1.11)	success	✅
pl-cpu (macOS-11, lightning, 3.9, 1.12)	success	✅
pl-cpu (macOS-11, lightning, 3.10, 1.13)	success	✅
pl-cpu (macOS-11, lightning, 3.10, 2.0)	success	✅
pl-cpu (macOS-11, lightning, 3.8, 1.11, oldest)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.8, 1.11)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.9, 1.12)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.10, 1.13)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.10, 2.0)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.8, 1.11, oldest)	success	✅
pl-cpu (windows-2022, lightning, 3.8, 1.11)	success	✅
pl-cpu (windows-2022, lightning, 3.9, 1.12)	success	✅
pl-cpu (windows-2022, lightning, 3.10, 1.13)	success	✅
pl-cpu (windows-2022, lightning, 3.10, 2.0)	success	✅
pl-cpu (windows-2022, lightning, 3.8, 1.11, oldest)	success	✅
pl-cpu (macOS-11, pytorch, 3.8, 1.13)	success	✅
pl-cpu (ubuntu-20.04, pytorch, 3.8, 1.13)	success	✅
pl-cpu (windows-2022, pytorch, 3.8, 1.13)	success	✅

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py, tests/tests_pytorch/strategies/test_fsdp.py.

🟢 pytorch_lightning: Azure GPU

Check ID	Status
[pytorch-lightning (GPUs) (testing Lightning	latest)](https://dev.azure.com/Lightning-AI/72ab7ed8-b00f-4b6e-b131-3388f7ffafa7/_build/results?buildId=171269&view=logs&jobId=47e66f3c-897a-5428-da11-bf5c7745762e)	success
[pytorch-lightning (GPUs) (testing PyTorch	latest)](https://dev.azure.com/Lightning-AI/72ab7ed8-b00f-4b6e-b131-3388f7ffafa7/_build/results?buildId=171269&view=logs&jobId=3f274fac-2e11-54ca-487e-194c91f3ae9f)	success

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py, tests/tests_pytorch/strategies/test_fsdp.py.

🟢 pytorch_lightning: Benchmarks

Check ID	Status
lightning.Benchmarks	success	✅

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py.

🟢 pytorch_lightning: Docs

Check ID	Status
docs-checks (pytorch, doctest)	success	✅
make-html (pytorch)	success	✅

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py.

🟢 mypy

Check ID	Status
mypy	success	✅

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py.

🟢 install

Check ID	Status
install-pkg (ubuntu-22.04, app, 3.8)	success	✅
install-pkg (ubuntu-22.04, app, 3.10)	success	✅
install-pkg (ubuntu-22.04, fabric, 3.8)	success	✅
install-pkg (ubuntu-22.04, fabric, 3.10)	success	✅
install-pkg (ubuntu-22.04, pytorch, 3.8)	success	✅
install-pkg (ubuntu-22.04, pytorch, 3.10)	success	✅
install-pkg (ubuntu-22.04, lightning, 3.8)	success	✅
install-pkg (ubuntu-22.04, lightning, 3.10)	success	✅
install-pkg (ubuntu-22.04, notset, 3.8)	success	✅
install-pkg (ubuntu-22.04, notset, 3.10)	success	✅
install-pkg (macOS-12, app, 3.8)	success	✅
install-pkg (macOS-12, app, 3.10)	success	✅
install-pkg (macOS-12, fabric, 3.8)	success	✅
install-pkg (macOS-12, fabric, 3.10)	success	✅
install-pkg (macOS-12, pytorch, 3.8)	success	✅
install-pkg (macOS-12, pytorch, 3.10)	success	✅
install-pkg (macOS-12, lightning, 3.8)	success	✅
install-pkg (macOS-12, lightning, 3.10)	success	✅
install-pkg (macOS-12, notset, 3.8)	success	✅
install-pkg (macOS-12, notset, 3.10)	success	✅
install-pkg (windows-2022, app, 3.8)	success	✅
install-pkg (windows-2022, app, 3.10)	success	✅
install-pkg (windows-2022, fabric, 3.8)	success	✅
install-pkg (windows-2022, fabric, 3.10)	success	✅
install-pkg (windows-2022, pytorch, 3.8)	success	✅
install-pkg (windows-2022, pytorch, 3.10)	success	✅
install-pkg (windows-2022, lightning, 3.8)	success	✅
install-pkg (windows-2022, lightning, 3.10)	success	✅
install-pkg (windows-2022, notset, 3.8)	success	✅
install-pkg (windows-2022, notset, 3.10)	success	✅

These checks are required after the changes to src/lightning/pytorch/strategies/fsdp.py.

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Thank you for your contribution! 💜

Note
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[carmocca]

This feature will likely be shortlived, but it's fine to add until the replacement is in