fix: improve types and remove path-exists dependency

[outslept]

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Summary

Refactor the functions-utils package to fix linting & types and remove the external path-exists dependency.

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[outslept]

off topic: based on the logs, the nudge action expects comment-tag but the current workflow uses comment_tag. perhaps this param can be updated in the future?

and regarding the failing edge-bundler test - it should be unrelated to my changes.

[mrstork]

off topic: based on the logs, the nudge action expects comment-tag but the current workflow uses comment_tag. perhaps this param can be updated in the future?

Thank you! I'll look into correcting this separate from your changes

and regarding the failing edge-bundler test - it should be unrelated to my changes.

Correct, we unfortunately have some flakiness in our test suite currently. I've cleared that red x up for you