fix(apiproxy): stop projecting injected context as user steering

next-step items now split by origin: user-origin messages keep the
'steering' placement, while agent.inject context (approval notices, task
completion notices, attached snapshots) carries a new 'context' placement
that no surface renders until it is claimed as a durable user/message
context card. Widen the placement unions on the wire and in the client
runtime, add a projection test case, and document the split in the
apiproxy/ui-conversation READMEs and the web-steer chrome agent note.

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

@@ -786,7 +786,14 @@ export function createApiProxy(ctx: Context, defaults: ApiProxyDefaults): ApiPro
     }
     return [
       ...project('next-turn').map(message => ({ id: message.id, placement: 'queued' as const, message })),
-      ...project('next-step').map(message => ({ id: message.id, placement: 'steering' as const, message })),
+      ...project('next-step').map(message => ({
+        id: message.id,
+        // Only user-origin messages are steering; injected context (approval
+        // notices, task completion, attached snapshots) is not a user action
+        // and must not render as a pending steering bubble.
+        placement: message.source.kind === 'user' ? 'steering' as const : 'context' as const,
+        message,
+      })),
     ]
   }