fix(telemetry): stamp a compaction on entering the null window

Claude Code's tracker nulls recache_tokens_if_cold at a compaction or a tool-result clearing and only counts the expected rebuild at the next request, which also closes the window, so no report carried both and the old rule never fired. Stamp on the first warm null report after one that carried a value, carry it through idle re-reports and drop it at the next request; the readout now says "Context compacted at HH:MM" since a clearing opens the same window.

Also persist a changed report so a crash restores the latest one, rename the session field to statusLineExporter (statusLineTelemetry is the registry capability) and document its values, word the stake as re-cached, move the readout block above the SSE staleness heading, and drop keep-warm mentions until it lands.

src/session.ts

@@ -1443,28 +1443,21 @@ export class Session extends EventEmitter {
 
   /**
    * Replace the prompt-cache report; true when it differs from the previous one. Stamps
-   * `compactedAt` when this report shows Claude Code's own idle compaction of the current
-   * prefix: `recacheTokensIfCold` is null (the transient post-compaction window the docs
-   * describe) while `expectedRebuilds` rose above the last report. The stamp is carried
-   * forward while that window holds, so the readout can say "compacted at HH:MM"; it is
-   * never an alert. A tool-result clearing bumps `expectedRebuilds` the same way, which the
-   * readout wording tolerates.
+   * `compactedAt` when this report ENTERS the window in which Claude Code reads
+   * `recacheTokensIfCold` as null: a compaction (`/compact` or its own idle compaction) or
+   * a clearing of old tool results opened it, and the previous report still had a known
+   * value. Claude Code closes the window on the next request (that request is the one that
+   * counts as an expected rebuild), so `expectedRebuilds` never rises inside it and is not
+   * read here. The stamp is carried while the window holds and dropped once it closes; a
+   * first report already inside the window gets none. It is never an alert.
    */
   setPromptCache(status: PromptCacheStatus): boolean {
     const prev = this._promptCache;
-    const inPostCompactWindow = status.recacheTokensIfCold == null && status.warm;
+    const inWindow = status.warm && status.recacheTokensIfCold == null;
     let compactedAt: number | undefined;
-    // A rise is only a rise against a KNOWN prior counter. Treating an absent prior as 0
-    // would invent a compaction out of the first report that already carries a high count
-    // (a restart mid-session, or `4 -> omitted -> 4`), so both counters must be present.
-    if (
-      inPostCompactWindow &&
-      prev?.expectedRebuilds != null &&
-      status.expectedRebuilds != null &&
-      status.expectedRebuilds > prev.expectedRebuilds
-    ) {
+    if (inWindow && prev?.recacheTokensIfCold != null) {
       compactedAt = Date.now();
-    } else if (prev?.compactedAt != null && inPostCompactWindow && status.expectedRebuilds === prev.expectedRebuilds) {
+    } else if (inWindow && prev?.compactedAt != null) {
       compactedAt = prev.compactedAt;
     }
     // A NEW object when a stamp applies, never a mutation of the caller's parsed report: the
@@ -1956,7 +1949,7 @@ export class Session extends EventEmitter {
       autoResumeEnabled: this._autoOps.autoResumeEnabled,
       autoResumeAt: this._autoOps.autoResumeAt ?? undefined,
       promptCache: this._promptCache ?? undefined,
-      statusLineTelemetry: this._muxSession?.statusLine,
+      statusLineExporter: this._muxSession?.statusLine,
       imageWatcherEnabled: this._imageWatcherEnabled,
       pinned: this._pinned || undefined,
       pinnedAt: this._pinned ? (this._pinnedAt ?? undefined) : undefined,