[CLI] Save only the configuration used

[carmocca]

What does this PR do?

Fixes #11463

Does your PR introduce any breaking changes? If yes, please list them.

The saved config format changes so this would be a breaking change if somebody relied on it.

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cc @Borda @carmocca @mauvilsa

[awaelchli]

The linked issue is the wrong one. There must be a typo :)

[tchaton]

LGTM !