Interactivity API: Update loading bar to use private router store

[luisherranz]

The Interactivity Router store contains internal properties (state.navigation.hasStarted, state.navigation.hasFinished) that are not part of the public API. Gutenberg PR #70882 moves these properties to a new private core/router/private store and adds deprecation warnings when they are accessed through the public core/router store.

This PR updates the loading bar markup in WP_Interactivity_API::print_router_markup() to use data-wp-interactive="core/router/private" instead of data-wp-interactive="core/router", so it accesses the private store directly and avoids triggering the deprecation warnings.

Trac ticket: https://core.trac.wordpress.org/ticket/64647
Related Gutenberg PR: WordPress/gutenberg#70882

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Props luisherranz.

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[github-actions]

A commit was made that fixes the Trac ticket referenced in the description of this pull request.

SVN changeset: 61653
GitHub commit: 0b8bc64

This PR will be closed, but please confirm the accuracy of this and reopen if there is more work to be done.

[luisherranz]

Thanks, Weston! 🙏❤️