feat: choose a product's category from the ones T5DE has seen

A product can be filed under another IMVU category than its parent's: any category path the hub has seen on a
revision's parent (and each step of it), within the parent's top-level category, so it stays the same kind of
product (the proxy tells clothing, furniture and rooms apart by category). It's an info field like the others:
lockable, in the history, undone by the same rules. Lists filter by the chosen path, and products show it.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

docs/design.md

@@ -473,8 +473,9 @@ Phases for products, catalogs and imports (products.md, console.md, imports.md):
    **Done** (2026-11-05), except catalog deletion requests and the hosted rooms' scope, which come with cases
    (phase 3). Built-in roles are code (`apps/api/src/permissions.ts`); the `role` table comes with custom roles.
 2. Product info: drafts, moderator edits with reasons and locks, info history, unlisted products, tags and category.
-   **Done** (2026-11-05), except a product's own category: the hub has no list of IMVU's categories to choose from,
-   so products are filed under their parent's category path for now (later: IMVU's category tree, cached).
+   **Done** (2026-11-05). A product's category is chosen from the IMVU category paths the hub has seen on parents,
+   within its parent's top-level category; IMVU's own category tree (if it has a public one) would replace those
+   (to look into with the importer spike).
 3. Cases (reports, appeals, reviews), file blocks and the catalogs' changes feed; notifications; API tokens;
    two-factor sign-in for sensitive permissions.
 4. Imports: grants, recorded grants, requests, unclaimed creators, the job queue, `t5de-importer` (after its spike).