refactor(tools): migrate producers to shared metadata bridge

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/tools/delegate-task/background-continuation.ts

@@ -1,9 +1,8 @@
 import type { DelegateTaskArgs, ToolContextWithMetadata } from "./types"
 import type { ExecutorContext, ParentContext } from "./executor-types"
-import { storeToolMetadata } from "../../features/tool-metadata-store"
+import { publishToolMetadata } from "../../features/tool-metadata-store"
 import { formatDetailedError } from "./error-formatting"
 import { getSessionTools } from "../../shared/session-tools-store"
-import { resolveCallID } from "./resolve-call-id"
 
 export async function executeBackgroundContinuation(
   args: DelegateTaskArgs,
@@ -37,11 +36,7 @@ export async function executeBackgroundContinuation(
         model: task.model ? { providerID: task.model.providerID, modelID: task.model.modelID } : undefined,
       },
     }
-    await ctx.metadata?.(bgContMeta)
-    const callID = resolveCallID(ctx)
-    if (callID) {
-      storeToolMetadata(ctx.sessionID, callID, bgContMeta)
-    }
+    await publishToolMetadata(ctx, bgContMeta)
 
     return `Background task continued.