docs(ai): partition ai.md into five subsystem files (verbatim moves)

ai.md 1,308 → 228 lines. No prose rewritten: every block was moved as-is so
nothing could be lost in translation, then replaced by a pointer.

New files:
- docs/ai/environment.md — LAN/SSH + Gitea push recipe, Windows dotnet
  build/run, test-suite map, hermetic real-MainWindow test rule
- docs/ai/product.md — brand/naming, AI transparency, GPL licensing
  prohibitions, free-forever monetization, auth/account assumptions,
  packaging & distribution
- docs/ai/youtube-api.md — go-live ordering, the broadcast-binding fix, the
  private-only lock, health parsing, end-stream pre-flight, Test mode,
  chat insert shape
- docs/ai/overlays.md — social bar, native alert box (animations, clip,
  ticker), chat box conventions
- docs/ai/ui-surface.md — control surface, scene strip, preview rail,
  hotkeys, broadcast drawer, toasts, transitions, brand logo, launch
  geometry, theme/properties conventions

ai.md keeps the response/derivation rules, the architecture table, the four
existing invariant stubs, and one pointer per moved subsystem.
docs/ai/index.md routes every file with a "read when" column.

References falsified by the move were fixed in the same commit: AGENTS.md
build note → environment.md → Run, and the "Related" footers in
frame-pipeline.md / output.md / capture.md now point at the owning files.

Docs-only unit: scope-check run, no build (no source touched).

docs/ai/output.md

@@ -319,8 +319,10 @@ devices, no timers).
   pipe and mute silences the loopback).
 ---
 
-## Related in [`ai.md`](../../ai.md) and [`frame-pipeline.md`](frame-pipeline.md)
+## Related files
 
 - [`frame-pipeline.md`](frame-pipeline.md) — the `FramePump` that feeds this encoder (pacing, backpressure, teardown order).
-- **ai.md** — resolution tiers (W×H/FPS/bitrate), go-live/prep ordering, toast notifications, licensing guardrails.
+- [`ui-surface.md`](ui-surface.md) — resolution tiers (W×H/FPS/bitrate) and toast notifications.
+- [`youtube-api.md`](youtube-api.md) — go-live/prep ordering and the broadcast lifecycle.
+- [`product.md`](product.md) — licensing guardrails (the ffmpeg pin, LGPL obligations).
 - [`TASKS/research-store-certification.md`](../../TASKS/research-store-certification.md) — §4, the ffmpeg bundling analysis.