Remove use of jsonargparse internals

[mauvilsa]

What does this PR do?

The import_docstring_parse function is not part of the jsonargparse public API, see https://jsonargparse.readthedocs.io/en/stable/#api-reference. This pull request removes its use to avoid possible failures due to changes in jsonargparse internals. An example of this happening can be seen in #12884 (comment).

I think this change should be included in 1.6.X. Even though import_docstring_parse is internal, I will change it again to be backward compatible so that released versions of LightningCLI do not fail due to this, see jsonargparse/commit/6dc8539.

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

None

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