Generated and pasted board backgrounds move into .backgrounds/ — the board root stops collecting the app's own pictures

New app-written background images (Theme tab ▸ Pattern, and Edit ▸ Paste
as Board Background) now land in a hidden `.backgrounds/` folder at
board root instead of beside index.md, matching the `.trash/` app-managed
pattern. `background.image` stores the qualified relative reference
(`.backgrounds/facets.png`); the resolver needed no change at all, since
it already accepted any relative path inside the board root — the same
mechanism that already resolved `art/backdrops/sunset.png` resolves the
new location for free. `BoardWriter.writeBoardImage` now creates its
destination folder if missing, since `.backgrounds/` won't exist until a
board's first generated or pasted background.

The Finder collision-ladder (`BoardStore.boardImageName`) is rescoped to
`.backgrounds/`'s own contents, and its overwrite-in-place check now
recognizes only the qualified form as "ours" — a legacy bare
`background.image: facets.png` from before this change is read as a
foreign reference rather than migrated, so a regeneration writes a fresh
`.backgrounds/` file and orphans the old one in place, per the no-migration
ruling. The Theme tab's Pattern/Solid mode-detection was updated to
recognize both the legacy and current spellings as the generator's own
output.

The board loader needed no change: `.backgrounds/` is a hidden,
non-UUID-shaped name, and `.skipsHiddenFiles` already keeps every hidden
entry off the lane walk before any name-based exclusion is consulted —
pinned with a new loader test. Deliberately did not add `.backgrounds` to
IntegrityRules' claimed-name/squatter-displacement table: that table
mirrors a specific existing DESIGN ruling this card doesn't amend.

Claude-Session: https://claude.ai/code/session_014PtZdPwqZuqEDLc6wZMtEy

Kanban/UI/Board/Backgrounds/BoardThemeTabView.swift

@@ -145,7 +145,15 @@ struct BoardThemeTabView: View {
         // Pattern, since that is the surface that made it; every other board — no image, or a
         // hand-placed one the app does not own — opens on Solid color, which is also the mode that
         // never overwrites a foreign picture by accident.
-        _mode = State(initialValue: store.snapshot.backgroundImage.value == FacetsGenerator.fileName ? .pattern : .solid)
+        //
+        // Two spellings answer "is it ours" since the `.backgrounds/` ruling (2026-08-09): the
+        // qualified reference every current write lands at (`BoardStore.boardImageName`), and the
+        // legacy bare name a board written before that ruling still carries at board root — a board
+        // moved from neither location by this check, so both keep opening on Pattern.
+        let image = store.snapshot.backgroundImage.value
+        let generatesThisImage = image == FacetsGenerator.fileName
+            || image == "\(BoardBackdrop.backgroundsFolderName)/\(FacetsGenerator.fileName)"
+        _mode = State(initialValue: generatesThisImage ? .pattern : .solid)
     }
 
     var body: some View {