fix: Operation copy-to-clipboard icon visibility.

[Azquelt]

Description

• Fix the doubling of the copy-to-clipboard icon by removing the inner svg element, and just leaving the button background.
• Allow the copy button to shrink to being invisible by removing its padding.
• Clean up the unused CopyIcon component.

Motivation and Context

Fixes #11046

How Has This Been Tested?

Tested manually in Firefox 155 and Chrome 153

Ran npm run cy:ci to check existing tests were not impacted.

Screenshots (if appropriate):

Operation:

Curl command:

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Checklist

My PR contains...

• No code changes (src/ is unmodified: changes to documentation, CI, metadata, etc.)
• Dependency changes (any modification to dependencies in package.json)
• Bug fixes (non-breaking change which fixes an issue)
• Improvements (misc. changes to existing features)
• Features (non-breaking change which adds functionality)

My changes...

• are breaking changes to a public API (config options, System API, major UI change, etc).
• are breaking changes to a private API (Redux, component props, utility functions, etc.).
• are breaking changes to a developer API (npm script behavior changes, new dev system dependencies, etc).
• are not breaking changes.

Documentation

• My changes do not require a change to the project documentation.
• My changes require a change to the project documentation.
• If yes to above: I have updated the documentation accordingly.

Automated tests

• My changes can not or do not need to be tested.
• My changes can and should be tested by unit and/or integration tests.
• If yes to above: I have added tests to cover my changes.
• If yes to above: I have taken care to cover edge cases in my tests.
• All new and existing tests passed.