fix(desktop): seed agent terminal tabs from process snapshots

Read-only agent terminal tabs now consume both live agent.terminal.output chunks
and the process-list/status snapshot. The snapshot seeds tabs opened after output
already exists and acts as a fallback if the live stream races startup, so agent
background tabs don't sit blank while the status stack already knows the tail.

apps/desktop/src/app/right-sidebar/terminal/agent-terminal-stream.ts

@@ -40,3 +40,29 @@ export function writeAgentTerminalChunk(procId: string, chunk: string): void {
   backlog.set(procId, next.length > MAX_BACKLOG ? next.slice(-MAX_BACKLOG) : next)
   writers.get(procId)?.(chunk)
 }
+
+/** Ingest a full output snapshot from process.list/status-stack. This is the
+ *  fallback for older/not-yet-restarted gateways and a seed for tabs opened
+ *  after output already exists. If it extends our current backlog, append only
+ *  the delta; if the registry's rolling tail slid, reset to that tail. */
+export function syncAgentTerminalSnapshot(procId: string, output: string): void {
+  if (!procId || !output) {
+    return
+  }
+
+  const current = backlog.get(procId) ?? ''
+
+  if (output === current) {
+    return
+  }
+
+  if (output.startsWith(current)) {
+    writeAgentTerminalChunk(procId, output.slice(current.length))
+
+    return
+  }
+
+  const next = output.length > MAX_BACKLOG ? output.slice(-MAX_BACKLOG) : output
+  backlog.set(procId, next)
+  writers.get(procId)?.(`\x1bc${next}`)
+}

apps/desktop/src/app/right-sidebar/terminal/workspace.tsx

@@ -3,6 +3,7 @@ import { useEffect } from 'react'
 
 import { $backgroundStatusBySession } from '@/store/composer-status'
 
+import { syncAgentTerminalSnapshot } from './agent-terminal-stream'
 import { setActiveTerminalId } from './buffer'
 import { AgentTerminalInstance, TerminalInstance } from './instance'
 import { $activeTerminalId, $terminals, ensureAgentTerminal } from './terminals'
@@ -30,12 +31,14 @@ export function TerminalWorkspace({ onAddSelectionToChat }: TerminalWorkspacePro
     }
   }, [])
 
-  // Surface the agent's background processes as read-only tabs (once each); their
-  // output streams in live via agent.terminal.output, no polling needed.
+  // Surface the agent's background processes as read-only tabs (once each).
+  // Live chunks stream via agent.terminal.output; the process-list snapshot also
+  // seeds/falls back so the tab never stays blank if the stream races startup.
   useEffect(() => {
     for (const list of Object.values(background)) {
       for (const item of list) {
         ensureAgentTerminal(item.id, item.title)
+        syncAgentTerminalSnapshot(item.id, item.output ?? '')
       }
     }
   }, [background])