Draft: Migrate icons to the Icons API (requires Drupal 11.1)

Aaron Christianrequested to merge
issue/bootstrap_ui_kit-3622922:3622922-icons-api into 2.x

Moves the UI Kit icons to core's Icons API. Ships with the Drupal 11.1 core version bump; rebase once !35 (merged) lands.

Closes #3622922

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