feat(live-sync): path-activate heartbeat on dotfiles writes (Refs #11)

Timer-only heartbeat left GUI dotfiles edits uncommitted for up to 59
minutes; a trunk-sync session clearing the dirty tree on 2026-10-18
destroyed a month of uncommitted noctalia bar layout inside that gap.
live-sync.path (DirectoryNotEmpty on dotfiles/) fires the existing
flock-guarded oneshot within seconds of any repo-side dotfiles write,
shrinking the exposure window from ~1h to ~2s. Timer stays as the
hourly catch-all for the machine tiers.

omp-docs/tools/live-sync.md

@@ -26,6 +26,13 @@ because the dirty tree collided with incoming work.
 machine's own writes on a schedule. Tier law (which paths it may touch) lives
 in [AGENTS.md](../../AGENTS.md) § Live-sync tiers.
 
+`live-sync.path` (`DirectoryNotEmpty` on `dotfiles/`) activates the same
+service within seconds of any GUI dotfiles write; `live-sync.timer` remains
+the hourly catch-all for the machine tiers the path unit does not watch.
+The trigger gap between a GUI edit and its commit is what let a 2026-10-18
+trunk-sync stash destroy a month of uncommitted bar layout — a timer-only
+heartbeat leaves up to 59 minutes of exposure.
+
 ## Contract (black-box)
 
 Run = one pass: flock → branch guard (`main` only) → stage allowlisted dirty
@@ -61,6 +68,7 @@ with the usual dotfiles chain:
 
 ```bash
 systemctl --user enable --now live-sync.timer   # after the unit is linked
+systemctl --user enable --now live-sync.path    # sub-second dotfiles trigger
 systemctl --user start live-sync.service        # one manual heartbeat
 journalctl --user -u live-sync.service -n 20    # observe
 ```