Carousels++

## Summary

Supports retention via browse & discovery.

Site-level carousel and facet improvements, grouped as one epic so the work has a single home on the [2026 Tracker](https://github.com/orgs/internetarchive/projects/21) rather than several unrelated issues.

Raised in the [2026 H2 planning recap](https://github.com/internetarchive/openlibrary/issues/13194#issuecomment-5062078256), where carousels/facets appear under August as "BearSunny's (Minh)'s site-level facets & carousels improvements w/ Lokesh".

## Scope

**New work**

- [ ] #10512 — Add Dropdown Menu to Facet Carousels (design proposal; currently `State: Blocked`, `Needs: Designs`)
- [ ] #13159 — Prototype: "Nearby Books" carousel, DDC shelf-adjacency browsing as a Lit component

**Correctness bugs**, inherited from #9828 (Carousel Fixups), which is closed in favour of tracking its remaining open items directly here:

- [ ] #5729 — Carousels don't follow merged work redirects (`Priority: 2`)
- [ ] #5731 — Works sometimes show up twice in a QueryCarousel that calls a subject tag (`Priority: 3`)
- [ ] #9342 — Work pulled in twice in collection carousel (`Priority: 4`)

## Notes

- #10512 and #13159 both carry `Needs: Designs`, so design input is the near-term gate on the new work, not engineering capacity.
- The three bugs above were the only issues still open under #9828; its other referenced items (#5858, #7252, #7552) were all closed during 2025.
- No lead is set yet: the planning note says "w/ Lokesh (?)" with the question mark, so ownership is still open.