Remove CPT name from permalink but add %category% instead

You have to set "hierarchical" => true in order to get %category% and %subcategory% to display:

"rewrite" => array(
    "slug" => "producten",
    "with_front" => false,
    "hierarchical" => true
),

Don’t forget to flush permalink settings by opening settings → permalinks and save.

More info: WordPress Codex: Function Reference/register post type

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