Build nested checkboxes

• Renders a tree of arbitrary depth from nested JSON (for example categories with children), with a checkbox per node and expand and collapse for parents
• Checking or unchecking a parent checks or unchecks all of its descendants
• A parent shows the checked state when all of its children are checked, unchecked when none are, and indeterminate when some are
• Changes propagate upward: toggling a leaf updates every ancestor's state
• State is derived from the leaf selection, not stored separately for every node, so it cannot get out of sync
• Clicking a label toggles its checkbox; keyboard Space toggles; the structure uses accessible roles (role="tree" or nested lists with labels)
• Exposes the list of selected leaf ids through onChange

Only after every requirement works.

• Expand all and collapse all, and a search box that filters the tree while keeping ancestors visible
• Lazy-load children when a node is expanded
• Preserve the selection when the data is replaced