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).

tests/e2e/mount.e2e.ts

@@ -288,6 +288,13 @@ test('plugin mounts into the DSH shell and survives a built-in tab sweep', async
     await assertNoCrash()
   }
 
+  // The sweep opened the Side Chat tab, whose view auto-creates a thread and
+  // polls the transcript — that poll MUST ride the plugin's own
+  // sidechat.events route (the DSH-0.1.2-safe transport this lane locks).
+  const polledTranscript = await page.evaluate(() =>
+    performance.getEntriesByType('resource').some(entry => entry.name.includes('/sidebar/api/sidechat.events')))
+  expect(polledTranscript, 'the Side Chat tab must poll sidechat.events for its transcript').toBe(true)
+
   // Side Chat host-route smoke against the REAL host: create a thread child
   // under the seeded session (custom-seed creation through AgentRegistry),
   // deliver a follow-up, cancel, and release it. The turn itself cannot run
@@ -315,12 +322,24 @@ test('plugin mounts into the DSH shell and survives a built-in tab sweep', async
     listedItems.some(item => item.sessionId === childId),
     'the thread child must appear in the host session list',
   ).toBe(true)
+  // Transcript read from the LIVE agent's log (the transport the tab polls;
+  // the inherited seed is cut host-side, so with no model route the own
+  // slice carries no message events).
+  const eventsLive = await api.post(sidebarApi('sidechat.events'), { data: { childId } })
+  expect(eventsLive.ok(), `sidechat.events (live): ${eventsLive.status()} ${await eventsLive.text()}`).toBe(true)
+  const eventsLiveBody = (await eventsLive.json()) as { ok: boolean; value?: { events?: Array<{ type: string }> } }
+  expect(eventsLiveBody.ok, `sidechat.events envelope: ${JSON.stringify(eventsLiveBody)}`).toBe(true)
+  expect(Array.isArray(eventsLiveBody.value?.events), 'sidechat.events must answer an events array').toBe(true)
   for (const method of ['sidechat.prompt', 'sidechat.cancel', 'sidechat.dispose']) {
     const response = await api.post(sidebarApi(method), {
       data: method === 'sidechat.prompt' ? { childId, text: 'follow-up' } : { childId },
     })
     expect(response.ok(), `${method}: ${response.status()} ${await response.text()}`).toBe(true)
   }
+  // After dispose the agent is gone: the same read must fall back to the
+  // PERSISTED log (the cold path a re-opened tab polls).
+  const eventsCold = await api.post(sidebarApi('sidechat.events'), { data: { childId } })
+  expect(eventsCold.ok(), `sidechat.events (cold): ${eventsCold.status()} ${await eventsCold.text()}`).toBe(true)
 
   // The Codex-style immediate-create flow: a blank question creates an
   // EMPTY thread (no prompt admitted), sidechat.info reports the live