Add log_key_prefix parameter to LearningRateMonitor

[Krishnachaitanyakc]

What does this PR do?

Adds a log_key_prefix parameter to the LearningRateMonitor callback, allowing users to prepend a configurable prefix to all logged metric names (learning rate, momentum, weight decay). This is useful for grouping learning rate metrics in loggers like TensorBoard.

Example:

lr_monitor = LearningRateMonitor(log_key_prefix="optim/")
# Logs "optim/lr-Adam" instead of "lr-Adam"

Fixes #21590

Changes

• src/lightning/pytorch/callbacks/lr_monitor.py: Added log_key_prefix parameter to __init__ and applied the prefix in _check_duplicates_and_update_name so it flows consistently through all metric keys (self.lrs, self.last_momentum_values, self.last_weight_decay_values, and logged metrics)
• tests/tests_pytorch/callbacks/test_lr_monitor.py: Added 4 test cases covering prefix with single optimizer, with momentum/weight_decay, with multiple optimizers, and with None (default behavior)
• src/lightning/pytorch/CHANGELOG.md: Added entry under [unreleased]

Before submitting

• Was this discussed/agreed via a GitHub issue? (prerfix for metric names the LearningRateMonitor #21590, maintainer @justusschock invited a PR)
• 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? (docstring updated)
• Did you write any new necessary tests? (4 new tests)
• Did you verify new and existing tests pass locally with your changes? (24 passed, 1 skipped)
• Did you update the CHANGELOG?

PR review

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📚 Documentation preview 📚: https://pytorch-lightning--21612.org.readthedocs.build/en/21612/

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 79%. Comparing base (612ab08) to head (451716a).
⚠️ Report is 1 commits behind head on master.
✅ All tests successful. No failed tests found.

❗ There is a different number of reports uploaded between BASE (612ab08) and HEAD (451716a). Click for more details.

HEAD has 920 uploads less than BASE

Flag	BASE (612ab08)	HEAD (451716a)
cpu	251	42
lightning_fabric	80	0
pytest	125	0
python3.12	72	12
python	18	3
lightning	90	15
python3.11	36	6
python3.13	53	9
python3.12.7	54	9
python3.10	18	3
pytorch_lightning	81	27
pytorch2.7	9	3
pytest-full	126	42
pytorch2.1	18	6
pytorch2.4.1	9	3
pytorch2.5.1	9	3
pytorch2.2.2	9	3
pytorch2.9	18	6
pytorch2.10	18	6
pytorch2.8	18	6
pytorch2.3	9	3
pytorch2.6	9	3

Additional details and impacted files

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- Misses       3220     5074   +1854