Fix LightningCLI failing when both module and data module save hyperparameters

[mauvilsa]

What does this PR do?

Fixes #20182

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📚 Documentation preview 📚: https://pytorch-lightning--20221.org.readthedocs.build/en/20221/

[lantiga]

LGTM, this is long overdue.

Just a suggestion and we're ready to merge

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 79%. Comparing base (60289d7) to head (1dc28c2).
Report is 1 commits behind head on master.

❗ There is a different number of reports uploaded between BASE (60289d7) and HEAD (1dc28c2). Click for more details.

HEAD has 102 uploads less than BASE

Flag	BASE (60289d7)	HEAD (1dc28c2)
cpu	48	24
lightning	37	18
pytest	26	0
python3.9	12	6
lightning_fabric	7	0
python3.11	12	6
python3.10	6	3
python3.12	18	9
gpu	2	0

Additional details and impacted files

@@            Coverage Diff            @@
##           master   #20221     +/-   ##
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- Coverage      88%      79%     -9%     
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  Files         267      264      -3     
  Lines       23382    23331     -51     
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- Hits        20479    18368   -2111     
- Misses       2903     4963   +2060