Replace fetch with wp.ajax.post

[chriscct7]

Fixes #125

This PR was written by AI and has not been reviewed yet for accuracy

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[chriscct7]

@ernilambar make sure you review this one thoroughly. We were testing an AI tool at Contributors Day that wrote the pr.

[ernilambar]

I tested this in my local setup and it is not working. Instead of returning data from AJAX, we get only Promise object.

[chriscct7]

Sounds good. I'll close this so we don't accidentally merge it