Fix spec violations in date_time_picker_input_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/date_time_picker/date_time_picker_input_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

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Related to #391077 (closed)