feat(lambda): use loggingFormat instead of logFormat

[tomoish]

The logFormat option in the FunctionOptions interface should accept one of the LogFormat enum options.

Since changing the logFormat type does not support languages other than TypeScript, This PR created a variable loggingFormat which has the correct type based on the discussion in #28127

However, I did not know how to build the code with this new variable. Therefore, I create PR in draft.

If anyone knows how to do this, your guidance would be greatly appreciated.
Thank you for your cooperation.

Closes #28114.

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