Remove outdated test selectors in CiIcon

What does this MR do and why?

This change removes some outdated test selectors that start with js- as well as some data-testid's in favor of selecting icons to verify CI statuses.

Why work on this?

I am implementing #377324 (closed) which shows some our running ci-icon in a new context. I'd like for the interface of ci-icon to be simpler for my used case so I find that adding validators and cleaning up the tests will help my effort.

Screenshots or screen recordings

NA

How to set up and validate locally

NA

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