fix(sidechat): read the transcript through the plugin's own events route

DSH 0.1.2-alpha.1 removed the client `ctx.connection.api` face (Remote
gateway migration), so every Side Chat transcript poll (`sessions.history`)
threw TypeError into the view's catch and was swallowed — the tab rendered
an empty transcript forever, silently (no console error, so the mount lane
never caught it). The successor APIs are not a drop-in either:
session/follow|page reject plain session addresses for origin:'subagent'
logs (agent-busy fence) and paging cannot read past the current cursor.

Move the transcript to the plugin's own wire — one transport for every
DSH generation:

- new `sidechat.events` route: live threads read the in-memory
  `agent.session.events`; cold threads read `sessionPersistence.inspect`
  (both seams exist since 0.1.0-rc.8; alpha.1's inspect returns the
  expanded logical log, never the packed chunk-row encoding). The
  inherited seed is cut host-side (`threadOwnLogEvents`), polls ride an
  `afterSeq` delta, and the response is tail-capped at 8000 events (the
  old client walk ceiling).
- SideChatView.fetchThread is single-path; collectOwnEvents (the client
  walk) is gone, and so are the ctx.connection mirror and inject entry
  (no consumer left).
- transcriptRows keeps re-cutting at session/end-seed as defense in
  depth.

Verification:
- unit: sidechat.events route (seed cut, afterSeq delta + never
  resurrecting the seed, cap, cold/live sources, 404/503/bad-request),
  full suite 1104 passed; typecheck and build (purity gate) green.
- mount e2e vs a real dsh-v0.1.2-alpha.1 source build: 14/14, including
  the Side Chat tab sweep polling sidechat.events (performance resource
  assertion) and live + post-dispose (persisted) route reads.
- mount e2e vs PATH dsh 0.1.0-rc.8: 14/14 (no regression).

src/client/api.ts

@@ -8,7 +8,7 @@
  */
 import { encodeHtmlUrl } from '../html-route.ts'
 import type { LastActivity } from '../subagent-activity.ts'
-import type { SidechatThreadInfo } from '../sidechat-core.ts'
+import type { SidechatLogEvent, SidechatThreadInfo } from '../sidechat-core.ts'
 import type { BrowserProbeResult } from './browser.ts'
 
 /** One wire failure. */
@@ -317,6 +317,14 @@ export const api = {
   /** Live state + agent identity (provider/model/preset) of a thread. */
   sidechatInfo: (childId: string) =>
     call<SidechatThreadInfo>('sidechat.info', { childId }),
+  /** One transcript pull of a Side Chat thread: the thread's OWN events
+   *  (the inherited seed is cut host-side and never crosses the wire).
+   *  `afterSeq` narrows the response to the delta beyond it (poll tail). */
+  sidechatEvents: (childId: string, afterSeq?: number, signal?: AbortSignal) =>
+    call<{ events: SidechatLogEvent[] }>('sidechat.events', {
+      childId,
+      ...(afterSeq !== undefined ? { afterSeq } : {}),
+    }, signal),
   /** The effective terminal shell and its display name (plugin-global). */
   shellGet: () =>
     call<{ shell: string; name: string }>('shell.get', {}),