revert(live-sync): drop path-activation unit

Frank veto: DirectoryNotEmpty re-fires on every file event (GUI writes,
wallpaper shuffle) un-debounced -> hundreds of heartbeat spawns/day.
The sweep is cheap (57 ms CPU) but the trigger design was event spam.
Exposure-window fix is an open design question; timer unchanged.

dotfiles/systemd-user/.config/systemd/user/live-sync.path

@@ -1,13 +0,0 @@
-[Unit]
-Description=Fire the live-sync heartbeat within seconds of a dotfiles-tier write
-
-[Path]
-# GUI writes (noctalia settings.toml, niri cfg) land in the repo via the
-# dotfiles symlinks; this directory watch makes "GUI edit -> durable commit"
-# sub-second instead of up to one heartbeat interval. DirectoryNotEmpty fires
-# while the dir holds any file, so the unit re-triggers on every modification
-# (the empty-dir edge case is irrelevant here — dotfiles is never empty).
-DirectoryNotEmpty=%h/.omp/dotfiles
-
-[Install]
-WantedBy=paths.target

omp-docs/tools/live-sync.md

@@ -26,13 +26,6 @@ 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
@@ -68,7 +61,6 @@ 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
 ```