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/host/apiproxy/src/api-proxy.ts

@@ -14,6 +14,7 @@ import type {
 import { createUserMessage, ReasoningEffortId } from '@deepseek-ai/dsh-llm'
 import { errorChain } from '@deepseek-ai/dsh-llm'
 import type { MessageId, MessageSource } from '@deepseek-ai/dsh-llm'
+import { lastActivityTime } from '@deepseek-ai/dsh-session'
 import type { Session, SessionEvent, SessionHeader, SessionId, UserMessage } from '@deepseek-ai/dsh-session'
 import type { SessionPersistence } from '@deepseek-ai/dsh-session-persistence'
 import type { Workspace, WorkspaceRecord } from '@deepseek-ai/dsh-workspace'
@@ -164,7 +165,9 @@ function sessionBlank(session: Session): boolean {
 function summarize(session: Session, running: boolean): SessionSummary {
   return {
     sessionId: session.id,
-    updatedAt: session.events.at(-1)?.time ?? session.header.createdAt,
+    // Excludes the inherited-history boundary: a resumed-but-untouched session
+    // must not sort as freshly worked in.
+    updatedAt: lastActivityTime(session.events) ?? session.header.createdAt,
     running,
     blank: sessionBlank(session),
     ...session.header.parentSession === undefined ? {} : { parentSessionId: session.header.parentSession },