compaction: the usage-anchored trigger + visible session state (round 15)

The relational-databases incident, diagnosed and fixed:

TRIGGER — pi's estimator law, adopted exactly: anchor on the last
assistant message's provider-reported usage (totalTokens || the field
sum) and chars/4-estimate ONLY what was appended after it. The anchor
scan skips aborted/zero-usage assistants and STOPS at the newest
compaction marker (pre-cut usage described context the next request
will not carry — pi's distrust rule). The old estimator
(JSON.stringify of every message /4) tripled the true context
(measured: 84,412 'tokens' estimated vs 38,799 provider-reported on
the incident record) — scaffolding, escaped LaTeX, thinking blocks
and app-side details all counted. estimateMessageTokens now counts
wire text only (text + thinking + toolCall name/args; content text
for user/toolResult/custom). The unanchored fallback runs the plain
heuristic over the CUT-HONORED projection plus the additive prompt
term; the anchored path adds nothing (usage already billed prompt
and tools).

OBSERVABILITY — compaction is a visible session-wide state (owner
spec): the transcript-bottom placeholder register gains COMPACTING
CONTEXT… (BrailleSpinner + Shimmer, the THINKING placeholder's twin,
mutually exclusive by construction — the gate precedes beginTurn),
and the sidebar row shows 'Compacting context · <ago>' with the
spinner (sessionMeta outranks busy; compacting-changed joins
turn-started/turn-settled as refresh triggers). Liveness rides the
API like turn-busy: ChatListItem.compacting + compactionInFlight on
both GET /api/chats and GET /api/chats/[id] (initiallyCompacting
covers the navigate-back-mid-compaction mount — the event already
fired), exported through the server barrel.

Also: the relational-databases record rolled back to pre-compaction
(marker, post-marker turns, tree reset; backup in /tmp) for a clean
retest. The summarizer-usage 'gap' was a misread — steps[] was
populated all along.

components/sidebar.tsx

@@ -243,6 +243,7 @@ export function timeAgo(iso: string, now = new Date()): string {
  *  still rides the API payload, so this is a one-line flip back if it's
  *  ever wanted. */
 function sessionMeta(chat: ChatListItem): string {
+	if (chat.compacting) return `Compacting context · ${timeAgo(chat.updatedAt)}`;
 	if (chat.pendingQuestion) return `Waiting for your answer · ${timeAgo(chat.updatedAt)}`;
 	if ((chat.kind ?? "teach") === "practice" && chat.pendingProblem) {
 		return `Problem waiting · ${timeAgo(chat.updatedAt)}`;
@@ -284,7 +285,7 @@ export function SessionRow({
 				kbdSelected && !active && "bg-accent/60 ring-1 ring-border",
 			)}
 		>
-			<SessionStatus busy={chat.busy} />
+			<SessionStatus busy={chat.busy || chat.compacting} />
 			<span className="min-w-0 flex-1">
 				{/* Titles are the learner's/teacher's WORDS — Source Sans 3, the
 				    same voice the words were typed in (every input is lh-prose);
@@ -486,6 +487,7 @@ function SessionsSidebar() {
 	useServerEvent("chats-changed", scheduleEventRefresh);
 	useServerEvent("turn-started", scheduleEventRefresh);
 	useServerEvent("turn-settled", scheduleEventRefresh);
+	useServerEvent("compaction-changed", scheduleEventRefresh);
 	useServerResync(() => void refreshRef.current());
 	useEffect(
 		() => () => {