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/types/session.ts

@@ -747,10 +747,12 @@ export interface PromptCacheStatus {
   /** Claude Code's diagnosis of the last miss, e.g. `ttl_expired_1h` or `tools_changed`. */
   lastMissCauses?: string[];
   /**
-   * Epoch MS when Codeman first saw Claude Code's own idle compaction for the current prefix
-   * (`recacheTokensIfCold` null while `expectedRebuilds` rose). Derived in `Session.setPromptCache`,
-   * not reported by the statusline, so it is never set by `parsePromptCache`. Lets the readout say
-   * "compacted at HH:MM"; it is never an alert (CC's idle compaction is benign).
+   * Epoch MS when Codeman saw the context compacted (`/compact`, Claude Code's own idle
+   * compaction, or a clearing of old tool results): the first warm report whose
+   * `recacheTokensIfCold` is null after one that carried it. Carried while the null window holds,
+   * dropped at the next request. Derived in `Session.setPromptCache`, not reported by the
+   * statusline, so it is never set by `parsePromptCache`. Lets the readout say "Context compacted
+   * at HH:MM"; it is never an alert.
    */
   compactedAt?: number;
 }
@@ -765,7 +767,7 @@ export interface PromptCacheStatus {
  *   statusLine (or could not be read), and Codeman never replaces one there.
  * - `remote`: remote and Docker launches never carry the exporter.
  */
-export type StatusLineTelemetry = 'injected' | 'collection-off' | 'workspace-statusline' | 'remote';
+export type StatusLineExporter = 'injected' | 'collection-off' | 'workspace-statusline' | 'remote';
 
 export interface SessionState {
   /** Unique session identifier */
@@ -826,8 +828,8 @@ export interface SessionState {
    * `expiresAt` has passed reads as cold rather than as a stale warm.
    */
   promptCache?: PromptCacheStatus;
-  /** Why a cache report will or will not arrive (see `StatusLineTelemetry`); absent when unknown. */
-  statusLineTelemetry?: StatusLineTelemetry;
+  /** Why a cache report will or will not arrive (see `StatusLineExporter`); absent when unknown. */
+  statusLineExporter?: StatusLineExporter;
   /** Pinned to the top of the session manager list (COD-139) */
   pinned?: boolean;
   /** When the session was pinned (epoch ms) — orders the pinned group, most-recent-first */