docs: update for Fabric

[Borda]

What does this PR do?

improve the user experience reading docs about Fabric

Before submitting

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• Did you make sure to update the documentation with your changes? (if necessary)
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📚 Documentation preview 📚: https://pytorch-lightning--21125.org.readthedocs.build/en/21125/

cc @justusschock @lantiga

[Copilot]

Pull Request Overview

This PR improves the documentation for PyTorch Lightning Fabric by adding comprehensive docstring enhancements and examples throughout the main Fabric class. The changes focus on making the API more user-friendly and accessible for developers.

• Enhanced docstrings with detailed parameter descriptions, default values, and return type information
• Added practical code examples for all major methods showing common usage patterns
• Improved error handling documentation with specific exception types and conditions

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[github-actions]

⚡ Required checks status: All passing 🟢

Groups summary

🟢 pytorch_lightning: Tests workflow

Check ID	Status
pl-cpu-guardian	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 pytorch_lightning: Azure GPU

Check ID	Status
pytorch-lightning (GPUs) (testing Lightning | latest)	success	✅
pytorch-lightning (GPUs) (testing PyTorch | oldest)	success	✅
pytorch-lightning (GPUs) (testing PyTorch | latest)	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 pytorch_lightning: Benchmarks

Check ID	Status
lightning.Benchmarks	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 fabric: Docs

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

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 lightning_fabric: CPU workflow

Check ID	Status
fabric-cpu-guardian	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 lightning_fabric: Azure GPU

Check ID	Status
lightning-fabric (GPUs) (testing Fabric | oldest)	success	✅
lightning-fabric (GPUs) (testing Fabric | latest)	success	✅
lightning-fabric (GPUs) (testing Lightning | latest)	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 mypy

Check ID	Status
mypy	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

🟢 install

Check ID	Status
install-pkg-guardian	success	✅

These checks are required after the changes to src/lightning/fabric/fabric.py.

---

Thank you for your contribution! 💜

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87%. Comparing base (da7f2f9) to head (3589553).
⚠️ Report is 9 commits behind head on master.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##           master   #21125   +/-   ##
=======================================
  Coverage      87%      87%           
=======================================
  Files         269      269           
  Lines       23560    23560           
=======================================
  Hits        20546    20546           
  Misses       3014     3014           

[lantiga]

Looks great