Icons: Allow registering icons that are hidden from the REST API with public property

[fushar]

Trac ticket: https://core.trac.wordpress.org/ticket/66087.
Backport from WordPress/gutenberg#82634.

What

This PR allows an optional boolean public property to icon registration via wp_register_icon().

Icons registered with public: false will still be available through wp_get_icon(), but the REST API will not return them, so they aren't exposed in the Icon block.

As a back-compatibility, if we don't provide a public property, the default is true and the behavior will be the same as the existing behavior.

Here's a summary of the behavior:

Registered with	Registry /wp_get_icon()	REST API / Icon block
public omitted or true	yes	yes
public: false	yes	no

Use of AI Tools

Used Claude Opus to generate the backported changes from the linked Gutenberg PR, then checked the changes myself.

[github-actions]

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[github-actions]

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Props fushar.

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