fix(sessions): read the composer from a styled capture so a prompt suggestion is not a draft

Claude Code draws its prompt suggestion in an empty composer, the first letter in the reverse-video cursor cell and the rest faint, so a plain capture read it as typed text and keep-warm never nudged those sessions. The keep-warm pane read now uses capture-pane -e and drops the suggestion before checking the composer.

Also from review: an off status carries no window, automation and an unreadable composer retry instead of stopping, a failed evaluation re-arms a retry, a trigger during an evaluation queues one follow-up that remove() cancels, and the cap's clock is seeded from lastSubmitAt for pre-upgrade state.

docs/wiki/Keeping-Agents-Running.md

@@ -111,7 +111,7 @@ Claude Code 2.1.251 and newer reports the cache state on the statusline after ev
 
 **Keep the cache warm while idle** is the switch under the readout. With it on, Codeman sends a one-line keep-alive turn (`Codeman cache keep-alive: no action needed, reply with just "ok".`) about five minutes before the cache would expire. Claude answers `ok`, the request refreshes the cache for another hour, and your next real prompt reads the conversation from cache instead of re-processing it. Measured on sessions of about 110k tokens, the keep-alive cost a cache read plus a one-word reply, a small fraction of the re-write it prevented.
 
-It only fires when there is nothing else going on: the session is idle with an empty prompt, no permission or question dialog is open, nobody has typed in the last few minutes, no respawn loop, Ralph loop or waiting agent is driving the session, and the session is not paused on a usage limit. If any of those hold it waits a minute and looks again, and gives up a minute before the expiry rather than race it. It also stops by itself a few hours after your last prompt (**Keep warm for at most**, under App Settings → System → Automation, default 2 hours), because the saving is concentrated in gaps of one to four hours and an overnight run of hourly keep-alives would cost more than the single cold turn in the morning. It stands down for the rest of a gap once the context has been compacted. The readout's Status line gains a `Keep-alive:` line that says what it is doing: the next keep-alive and when the window closes, waiting and why, sent at a time with a count, or stopped and why. A session started without the cache readout (Plan Usage off at launch, a workspace with its own statusLine, a remote or Docker session) cannot be kept warm: the switch is greyed out and cannot be switched on (one that is already on can still be switched off), and the Status line says why.
+It only fires when there is nothing else going on: the session is idle with an empty prompt (Claude Code's greyed-out prompt suggestion counts as empty), no permission or question dialog is open, nobody has typed in the last few minutes, no respawn loop, Ralph loop or waiting agent is driving the session, and the session is not paused on a usage limit. If any of those hold it waits a minute and looks again, and gives up a minute before the expiry rather than race it. It also stops by itself a few hours after your last prompt (**Keep warm for at most**, under App Settings → System → Automation, default 2 hours), because the saving is concentrated in gaps of one to four hours and an overnight run of hourly keep-alives would cost more than the single cold turn in the morning. It stands down for the rest of a gap once the context has been compacted. The readout's Status line gains a `Keep-alive:` line that says what it is doing: the next keep-alive and when the window closes, waiting and why, sent at a time with a count, or stopped and why. A session started without the cache readout (Plan Usage off at launch, a workspace with its own statusLine, a remote or Docker session) cannot be kept warm: the switch is greyed out and cannot be switched on (one that is already on can still be switched off), and the Status line says why.
 
 Recent Claude Code builds can compact a large idle session on their own shortly before the cache expires, which would leave only a summary to keep warm. So a session **started** with keep-warm on also launches with Claude Code's idle compaction switched off (Claude Code 2.1.290 or newer); Codeman then owns the idle policy for it. A session you switch on after it started is still kept warm, but Claude Code may compact it first until its next launch, and the Status line says so; one you switch off keeps Claude Code's idle compaction off until its next launch, and the Status line says that too. Sessions with keep-warm off launch exactly as before.