nudger: a schedule that keeps a chat moving when nobody is watching

an agent told to record blockers and continue still stops at the end of a
turn, and at 3am nobody types the next message. this is the schedule that does.

the door already existed. `startClaudeTurn` takes `ws: null` — extracted that
way so command-hq could drive a turn over http — so this is a second caller of
an existing path rather than a new way into a live session. i had said the
platform lacked that; it did not.

the rule that decides the design: never speak while the agent is working. so
`every_seconds` is a FLOOR, not a metronome. when a nudge comes due and the
session is generating, the row is left alone and reconsidered next tick, which
means it fires as soon as the turn ends rather than sleeping through to the
next hour. a strict alarm would skip an agent that finished four minutes late
and leave it idle for the other fifty-six.

`isGenerating` unknown counts as BUSY. a sidecar that cannot answer might be
mid-turn, and interrupting one is the failure this exists to avoid.

matched on both sessionKey and claudeSessionId: officer's handle and the
transcript's filename are different ids, only the agent holds the mapping, and
a schedule stored against one would silently never match a live row keyed by
the other.

one nudge per (user, session) — a second schedule for one conversation is two
alarms for one sleeper. counted even when the turn fails to start, so a
refusal cannot become a tight loop. disables itself at the ceiling rather than
leaving a spent row armed. the tick starts in server.tsx rather than on first
use, because a schedule armed before a restart has to survive one.

src/server.tsx

@@ -19,6 +19,7 @@ import { terminalWebsocket } from './servers/api/terminal/websocket';
 import { chatWebsocket } from './servers/api/chat/websocket';
 import { chatNotifyWebsocket } from './servers/api/chat/notify-delivery';
 import { registerChatPushNotifications } from './servers/api/chat/notify-push';
+import { startNudger } from './servers/api/chat/nudger';
 import { taskRunnerWebsocket } from './servers/api/tasks/task-executor';
 import { pipelineWebsocket } from './servers/api/tasks/pipeline-executor';
 // import { desktopWebsocket } from './servers/api/desktop/websocket';
@@ -166,6 +167,10 @@ assertPermissionTotality({
 // module whose only job is a side effect is one an import sweep quietly deletes.
 registerChatPushNotifications();
 
+// Nudger's tick. Here rather than on first use, because a schedule armed before a restart has to survive
+// one — the row is in Postgres and nothing else would ever look at it again.
+startNudger();
+
 // That the working directory is the repo, because every path derives from its parent. First of the three,
 // since a wrong answer here makes the other two check the wrong files.
 assertInstallLayout();