feat(plex): add a movie or show to a collection from its card menu

"Add to collection…" opens a panel beside the card: the title's library's
manual collections tick it in or out, and a name + Enter creates a new one with
the title in it. It used to take the Collections page, a new collection, its
name and a title search, then another search per title. A lean endpoint lists
the collections with whether each holds the title. Admin only, as on the
title's page.

Also: a collection seeded with a show is made as a show collection (Plex type
2). Measured: as a movie one it came out empty and refused the show after.

docs/DESIGN.md

@@ -714,3 +714,4 @@ of a full-width panel and nothing on the right.
 | 2026-10-08 | Captions on touch | A `Tooltip` opens for a mouse and a key's focus only, never for a finger | A caption on tap; a long-press caption | On an iPad the tap that showed the caption was taken as a hover and lost its click (every rail button took two taps), and no finger sends the mouseleave that hides it; the rail's labels setting names the buttons on touch |
 | 2026-10-08 | Header search on touch | No key cap on a touch screen; the pill grows to 52 px so a ring shows round the 44 px Go; Go drops to its icon by the column's width | Keep the key cap; a 44 px Go overhanging a 40 px pill | On a tablet the 44 px key cap and Go sat on the pill's edge and cut the placeholder; an overhanging Go breaks the nested radii |
 | 2026-10-08 | Plex subtitles and the control bar | The player draws the cues itself; while the bar shows they rise above it (200 ms), then settle back | The browser's own cues, moved by `line` | On an iPad the bar covered the text; a native cue cannot be animated or measured, and our layer behaves the same on every engine |
+| 2026-10-08 | Plex "Add to collection" | A movie or show card's menu row opens a panel beside the card: its library's manual collections tick in place, a name + Enter creates one with the title in it (admin; option A) | An Add submenu with a "New…" dialog; the per-title editor modal from the menu | A collection took a trip to the Collections page, a name, a title search, then a second search per title; the panel is the video card's "Add to playlist" |