feat(session): project the inherited-history boundary into the log

A plugin owning a standalone open/close bracket cannot tell a dead marker
from a live one: an unmatched `compact/start` reads identically whether the
previous writer died mid-compaction or a compaction is running now.
`Session.firstLiveSeq` already holds that answer exactly, but only in memory.

Append the log-only `session/inherited` event at that seq from the seeded
constructor — the single waist all six seeded-start paths pass through
(resume, configured startup on a persisted id, `sessions.fork()`, a subagent
fork child, `adopt()`'s live prefix, and a bare seeded `create`). Read it
through the new `isInheritedSeq(events, seq)`.

The constructor placement means persistence needs no changes: the marker is
already in `events` when a backend captures the creation seed, so it rides
the ordinary seed path with no load-time write. It also covers fork, where
the inherited bracket's owner may still be running — the case a
persistence-layer boundary could not reach.

Activity ordering excludes the boundary through `lastActivityTime()`, since
lazy resume makes browsing a pickup and the three call sites would otherwise
float every opened session to the top of a picker or list.

packages/ui/tui/src/index.ts

@@ -35,6 +35,7 @@ import type { ContentBlock, MessageId } from '@deepseek-ai/dsh-llm'
 import type {} from '@deepseek-ai/dsh-llm-retry'
 import { renderPrompt } from '@deepseek-ai/dsh-system-prompt'
 import {
+  lastActivityTime,
   SessionId,
   type SessionEvent,
   type UserMessage,
@@ -985,7 +986,7 @@ export function createTuiChat(
     const systemPrompt = displayText(renderPrompt(assembly)) || '(empty)'
     const registeredTools = assembly.tools.map(tool => displayText(tool.name)).join(', ') || '(none)'
     const events = agent.session.events
-    const latestActivity = events.at(-1)?.time ?? agent.session.header.createdAt
+    const latestActivity = lastActivityTime(events) ?? agent.session.header.createdAt
     const usedContext = Math.max(0, Math.round(ctx.tokenMeter.measure(agent.session).totalTokens))
     let context = `${formatDiagnosticNumber(usedContext)} used · capacity unknown`
     const contextWindow = modelController.contextWindow()