Fix spec violations in new_issue_dropdown_spec.js

What does this MR do and why?

Fixes spec violations in https://gitlab.com/gitlab-org/gitlab/-/tree/master/spec/frontend/vue_shared/components/new_issue_dropdown/new_issue_dropdown_spec.js by removing spy on component methods.

Screenshots or screen recordings

N/A

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #391075 (closed)