feat: migrate Manage Categories to the shared tile-ordering workflow

[devin-ai-integration]

Summary

Closes #982 (epic #975). Manage Categories no longer has its own ordering contract — it persists through the same coordinator + atomic PUT /api/tile-order path as Browse.

Before, a dialog drop persisted via two independent requests that could partially succeed:

handleDrop -> interleavedSortOrders() -> PUT /categories/reorder
                                      -> PUT /images/reorder

Now the drop is decomposed into parent moves and per-scope mixed orders:

handleDrop -> diffParentMoves() + interleavedTileOrders()
           -> reorderTilesFromManage(moves, scopes)   // useCategoryActions
                for each move:  PATCH /categories/{id} (versioned, validated move path)
                for each scope: tileOrderingCoordinator.reportOrder(scope, fullOrder)
                                  -> PUT /api/tile-order (CAS revision, one transaction)

Key pieces:

• interleavedTileOrders(newCats, oldCats, imagesByParent): ScopeOrder[] replaces interleavedSortOrders, emitting the full interleaved TileOrderItemRef[] per changed scope (image slots keep their positions; unchanged scopes are omitted).
• Move vs. reorder stays distinct: parent changes go first through the versioned category PATCH; only then are scope orders reported, so tile-order membership validation matches.
• The dialog renders sibling order from the coordinator's per-scope displayOrder (reorderFlatOptions + a coordinator subscription), so pending order doesn't snap back while a save is in flight, and shows the shared ReorderStatusIndicator (unsaved/saving/saved/conflict Refresh–Keep my order/error Retry) for the last-reordered scope.
• Legacy reorderCategoriesInline/reorderImagesInline wrappers are removed; no runtime frontend caller uses PUT /categories/reorder / PUT /images/reorder anymore. Remaining legacy surface (backend endpoints, api.ts wrappers, SortableTileGrid non-coordinator fallback used only by tests) is tracked for removal in chore: remove legacy per-entity reorder endpoints and SortableTileGrid fallback #998.
• docs/tile-ordering.md gains a "Manage Categories migration (Migrate Manage Categories to the shared ordering workflow and complete end-to-end verification #982)" section and updated legacy-endpoint notes.

Needs human verification (non-blocking): drag feel of the dialog tree with the coordinator-driven order, and the conflict UX ("Keep my order") when two tabs reorder the same scope from Browse and Manage simultaneously.

Refs #975.

Link to Devin session: https://app.devin.ai/sessions/414754bd88374dc693f47100ac269e78

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Devin Review found 4 new potential issues.