docs: restructure TASKS.md into a catalog — one file per task in TASKS/

TASKS.md is now the index (status table, open items, research pointer).
33 files: 32 task files + 1 research facts file. The full take-saga
narrative and all design decisions are preserved verbatim; the catalog
makes the queue readable without opening every task body. Schema and
AGENTS.md updated to reflect the new layout.

TASKS/task-16-kill-infinity-display.md

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+# TASK 16 — Kill infinity display (no-game backdrop fallback)
+
+> Catalog: [`TASKS.md`](../TASKS.md) — status and requirements live here.
+
+
+**Goal:** when no full-screen game is detected, show a static branded placeholder instead of
+capturing the primary display (which causes the infinity mirror effect).
+
+### Status: ✅ Shipped
+
+**Changes:**
+1. `ResolveAutoCaptureKey()` returns `null` when no full-screen game is detected (was: primary monitor)
+2. `ReacquireScreenCaptures()` — clears stale `CaptureKey` when `auto == null` (handles DB upgrades);
+   skips `AcquireAsync` when no keys are set
+3. `SeedLiveBackdropAsset()` — sets `AssetId` on the backdrop element itself (NOT a Background source);
+   called from `ReacquireScreenCaptures()` after `EnsureBackdrop()` guarantees the element exists
+4. `Source.DisplaySource` falls back to `_imageSource` when `VideoImageSource` is null for live captures
+5. `Assets/live-backdrop.jpg` — user-provided image, added as `<Resource>` in csproj
+6. `ResolveOutputFrame()` in compositor — `Source { IsLiveCapture: true, CaptureKey: not null }` already skips null keys; fallback pattern `Source { AssetId: not null }` picks up the static image
+
+**Rendering flow:**
+| Scenario | Preview | Compositor |
+|---|---|---|
+| Game detected | Live capture (opaque, covers static asset on backdrop) | `ScreenCaptureManager.GetLatestFrame` |
+| No game | Static image via `DisplaySource` → `_imageSource` on backdrop | `StaticPixelCache.Get(assetId)` |
+| Manual capture pick | Live capture | Live frame |
+