feat(web): client order view in the library (UI/UX feedback wanted)

Depends on #549. Only the feat(web): … commit is new here; the other commits are #549.

This adds a UI for the grouped client ordering in #549. Before I polish it I'd like your take on the UX.

What it does

The Library gets a Client order sort mode that previews exactly what /applist sends:

• Custom apps (Desktop, Steam Big Picture, …) reorder by drag or up/down buttons, using the existing /api/apps/reorder endpoint.
• Groups move up and down, and each integration has a sort picker: name, recently played, or most played.
• A banner offers to turn on legacy ordering, since Moonlight otherwise sorts A to Z.
• /api/apps gains a client_order field so the preview never disagrees with the host.

Screenshots are from the Vite dev server with a mocked API. Manual testing on a real host shortly.

Questions

1. Placement: is a sort mode in the Library the right home, or would you rather have a separate section, e.g. under Integrations or Settings?
2. Per-integration sort: in the Library group header (as here) or on each provider's Integrations card?
3. Legacy ordering: is it OK for the Library to flip the global legacy_ordering setting with a "Turn on" button, or should it only link to Settings?
4. Anything you'd cut, to keep the Library simpler?

e2e coverage is in e2e/ui.spec.ts (library client order groups sources and saves the custom order).

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