chore: convert api command to use clack

[khendrikse]

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Summary

This converts the api command into using the new NetlifyLog. It is part of a bigger piece of work that can be seen in #6293. This is also the reason why this PR is merged into the branch CP-101/design-system-clack-implementation. It's a way in which I'm trying to keep possible failing tests, but also the review work to a minimum amount of work for those who are reviewing.

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