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.

docs/wiki/Keeping-Agents-Running.md

@@ -105,7 +105,7 @@ subscription plan.
 
 Claude Code bills a turn against the cached conversation while that cache is warm, and lets the cache expire after a fixed idle time: one hour on a subscription within plan usage, five minutes on an API key, a cloud provider or extra-usage credits. The first turn after a longer break re-processes the whole context at the cache-write rate, which is why coming back to a big session after lunch costs more than the turns around it.
 
-Claude Code 2.1.251 and newer reports the cache state on the statusline after every response, and Codeman's statusline exporter keeps it per session. The row shows **Warm until HH:MM** with the lifetime and the tokens that would be re-read if it went cold, or **Cold** with the size of the re-read the next turn pays. When Claude reports them it also shows the session's cache hit rate and the cause of the last cache miss (for example `ttl_expired_1h` or `tools_changed`), so a surprise miss has a reason next to it. If the conversation is compacted while it stays warm (Claude Code now does this on its own on large idle sessions, and a manual `/compact` does it too), the row notes **Compacted at HH:MM**: the cache holds a smaller prefix, so there is nothing to re-read. None of this raises an alert. The row refreshes live and flips to cold on its own when the lifetime passes, and the last state is kept across a Codeman restart so it is not blank until the session's next turn. Sessions without a statusline of their own also get a short `cache:until HH:MM` or `cache:cold` group in the terminal footer. The readout rides the plan usage chip's telemetry collection, which is on by default on desktop.
+Claude Code 2.1.251 and newer reports the cache state on the statusline after every response, and Codeman's statusline exporter keeps it per session. The row shows **Warm until HH:MM** with the lifetime and the tokens that would be re-cached if it went cold, or **Cold** with the size of the re-cache the next turn pays. When Claude reports them it also shows the session's cache hit rate and the cause of the last cache miss (for example `ttl_expired_1h` or `tools_changed`), so a surprise miss has a reason next to it. If the conversation is compacted while it stays warm (Claude Code now does this on its own on large idle sessions, a manual `/compact` does it too, and so does a clearing of old tool results), the row notes **Context compacted at HH:MM** until the next turn: Claude Code reports no re-cache size until then. None of this raises an alert. The row refreshes live and flips to cold on its own when the lifetime passes, and the last state is kept across a Codeman restart so it is not blank until the session's next turn. Sessions without a statusline of their own also get a short `cache:until HH:MM` or `cache:cold` group in the terminal footer. The readout rides the plan usage chip's telemetry collection, which is on by default on desktop.
 
 ## The plan usage chip