feat(displays): hotplug auto-switch for display profiles (item 15b)

nomarchy-display-profile gains `match <outputs>`: an exact set match
wins, else the largest profile whose named outputs are all connected;
any tie prints nothing — the watcher must never flap between ambiguous
layouts. nomarchy-display-profile-watch (exec-once when profiles are
declared, the keyboard-watcher poll pattern — session units race
Hyprland IPC on relogin) reacts to output-set CHANGES only, reads
settings.displayProfileAuto from the live state each time (the menu's
new Auto-switch row toggles it instantly, no rebuild), and applies via
the tool — so an auto-pick persists a concrete profile that the next
rebuild bakes. A separate boolean rather than an "auto" pseudo-profile
for exactly that bake semantics.

Verified: V0 (flake check); V1 — a scratch 4-profile downstream builds;
tool + watcher pass bash -n; the match matrix exercised end-to-end:
three exact picks, an unambiguous-superset pick, a tie -> none, a
no-fit -> none; the watcher is exec-once'd in the rendered config; the
menu renders the Auto-switch row. Remains: V3 real dock/undock
(HARDWARE-QUEUE, rides the slice-a entry). Slice c (workspace binding)
stays, tagged optional.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

agent/BACKLOG.md

@@ -71,12 +71,14 @@ the *same* outputs. **Plan (designed 2026-07-05, iteration #27):**
 - **Slices:** (a) ✓ shipped 2026-07-05 (iteration #28): option +
   overlay (pure `modules/home/monitor-rules.nix`, unit-tested by
   checks.display-profiles) + `nomarchy-display-profile` applier + menu
-  Profiles row + template example — V3 (real dock) queued; (b)
-  opt-in hotplug auto-switch: a socket2 watcher on monitoradded/
-  removed picks the profile whose named-output set matches connected
-  outputs (exact match, else largest subset, ties = no switch) —
-  decide the flag shape (`settings.displayProfile = "auto"` vs a
-  separate boolean) at implementation; (c) optional per-profile
+  Profiles row + template example — V3 (real dock) queued; (b) ✓
+  shipped 2026-07-05 (iteration #29): hotplug auto-switch — `match`
+  subcommand (exact set, else unambiguous largest subset, ties =
+  none) + a poll watcher (exec-once, the keyboard-watcher pattern)
+  gated live on `settings.displayProfileAuto` (a separate boolean,
+  NOT an "auto" pseudo-profile, so auto-picks persist concrete
+  profiles that rebuilds bake) + menu Auto-switch row — V3 rides the
+  slice-a dock test; (c) optional per-profile
   `workspaces = { "1" = "DP-3"; }` → Hyprland `workspace` keywords.
 - **Non-goals:** no kanshi (fights Hyprland's output management —
   decided in ROADMAP), nwg-displays stays a find-the-values helper.