Update examples with multiple optimizers

[awaelchli]

What does this PR do?

Follow up to #16539. After multiple optimizers must be handled in manual optimization, we also need to update the two remaining examples we have.

I verified that the refactored code produces loss curves of the same shape as in the commit before #16539 by comparing the runs in TensorBoard.

Before submitting

• Was this discussed/approved via a GitHub issue? (not for typos and docs)
• Did you read the contributor guideline, Pull Request section?
• Did you make sure your PR does only one thing, instead of bundling different changes together?
• Did you make sure to update the documentation with your changes? (if necessary)
• Did you write any new necessary tests? (not for typos and docs)
• Did you verify new and existing tests pass locally with your changes?
• Did you update the CHANGELOG? (not for typos, docs, test updates, or internal minor changes/refactorings)

PR review

Anyone in the community is free to review the PR once the tests have passed.
Before you start reviewing make sure you have read Review guidelines. In short, see the following bullet-list:

• Is this pull request ready for review? (if not, please submit in draft mode)
• Check that all items from Before submitting are resolved
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Did you have fun?

I made sure I had fun coding 🙃

cc @Borda @justusschock @awaelchli

[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, 3.8, 1.11, oldest)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.9, 1.11)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.10, 1.12)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.10, 1.13)	success	✅
pl-cpu (ubuntu-20.04, lightning, 3.8, 1.11, oldest)	success	✅
pl-cpu (windows-2022, lightning, 3.9, 1.11)	success	✅
pl-cpu (windows-2022, lightning, 3.10, 1.12)	success	✅
pl-cpu (windows-2022, lightning, 3.10, 1.13)	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/demos/mnist_datamodule.py.

🟢 pytorch_lightning: Azure GPU

Check ID	Status
pytorch-lightning (GPUs)	success	✅

These checks are required after the changes to src/lightning/pytorch/demos/mnist_datamodule.py.

🟢 pytorch_lightning: Azure HPU

Check ID	Status
pytorch-lightning (HPUs)	success	✅

These checks are required after the changes to src/lightning/pytorch/demos/mnist_datamodule.py.

🟢 pytorch_lightning: Azure IPU

Check ID	Status
pytorch-lightning (IPUs)	success	✅

These checks are required after the changes to src/lightning/pytorch/demos/mnist_datamodule.py.

🟢 pytorch_lightning: Docs

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

These checks are required after the changes to src/lightning/pytorch/demos/mnist_datamodule.py.

🟢 mypy

Check ID	Status
mypy	success	✅

These checks are required after the changes to src/lightning/pytorch/demos/mnist_datamodule.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/demos/mnist_datamodule.py.

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Thank you for your contribution! 💜

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