docs(synlig): the transcript inbox is the primary's third moving part; and survive an unset HOME

Runbook gaps found while fixing the 2026-08-15 feed failure:

- §2.5 still titled "written but not installed" and still asserting "Not
  installed, not enabled" — false since 2026-08-12. A reader landing there got
  a flat contradiction of §4 item 3. Retitled, with the verified-2026-08-16
  process line, and it now states the fact §2.6 depends on: the server is a
  NATIVE process (no mempalace container on synlig), so it sees host paths.
- New §2.6 documents ~/mempalace-feed/<device>/: why transcripts cannot travel
  over the HTTPS leg at all, the three client variables, and why
  MEMPALACE_PI_REMOTE_PATH is the trap (its /data/feed default assumes a
  containerized server; here it must equal the ssh-target path, and a mismatch
  fails with rsync succeeding and only the mine failing). Plus the operational
  notes that cost time: dedup keys on the absolute path so the inbox path is
  load-bearing, grown sessions are purged+refiled by mtime, and a client-side
  MCP timeout is NOT a failed mine.
- Header status: counts refreshed with an explicit "treat counts as timestamps".

Also, bin/mempalace-pi-session: default HOME from the passwd database when it is
unset. `docker run --entrypoint="" <image>` inherits no HOME when the image
config declares none, and every default is HOME-anchored under `set -u`, so the
script — including the palace-free --self-test — died with "HOME: unbound
variable" in exactly the environment pi-devbox's smoke suite uses. pi-devbox
v1.8.0 lost a release to the same assumption from the other side.

bin/mempalace-pi-session

@@ -123,6 +123,17 @@
 
 set -euo pipefail
 
+# HOME can legitimately be unset: `docker run --entrypoint="" <image>` inherits
+# no HOME when the image config declares none (pi-devbox's does not — HOME is
+# normally set by its entrypoint, which --entrypoint="" skips), and every
+# default below is HOME-anchored under `set -u`, so the script died at line 1 of
+# real work with "HOME: unbound variable". Derive it from the passwd database —
+# exactly what python's expanduser() falls back to — so the script, and
+# especially the palace-free --self-test, runs in a bare container too.
+# pi-devbox v1.8.0 lost a release to this same "the image sets HOME" assumption.
+: "${HOME:=$(python3 -c 'import os, pwd; print(pwd.getpwuid(os.getuid()).pw_dir)' 2>/dev/null || echo /tmp)}"
+export HOME
+
 # ── Defaults ─────────────────────────────────────────────────────────
 AGENT="${USER:-mempalace}"
 WING="wing_conversations"