refactor(x): finish turn-spine adoption for headless surfaces

Background-task and live-note transcript views move from fetch-once to
the shared useAgentRunTranscript hook (useTurn over the turns:events
spine, with a one-shot legacy runs:fetch fallback for pre-migration run
ids), so an in-flight run's transcript now streams live. The headless
runner drains its execution stream — delivery rides the turn event bus,
and an unconsumed HotStream buffered every durable event until settle.
Deletes the caller-less runHeadlessTurn duplicate (HeadlessAgentRunner
is the implementation; session-design.md now says so) and the orphaned
web-search skill file that was never registered.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/x/packages/core/docs/session-design.md

@@ -376,7 +376,10 @@ which governs mutation of live logs, not their removal.
 ## 11. Headless standalone turns
 
 A helper covers the non-session callers (background tasks, live notes,
-knowledge pipelines, scheduled agents):
+knowledge pipelines, scheduled agents). Implemented as
+`HeadlessAgentRunner` in `agents/headless.ts` (start/run handle with
+turn id, reduced state, and final assistant text); the shape below is
+the contract it fulfils:
 
 ```ts
 function runHeadlessTurn(input: {

apps/x/packages/core/src/agents/headless.ts

@@ -163,6 +163,18 @@ export class HeadlessAgentRunner implements IHeadlessAgentRunner {
         const execution = this.turnRuntime.advanceTurn(turnId, undefined, {
             signal: options.signal,
         });
+        // Drain the execution stream: live delivery rides the turn event bus,
+        // and an unconsumed HotStream would buffer every durable event in
+        // memory until the turn settles.
+        void (async () => {
+            try {
+                for await (const event of execution.events) {
+                    void event;
+                }
+            } catch {
+                // Infrastructure failures surface through the outcome.
+            }
+        })();
         const done = execution.outcome.then(async (outcome) => {
             const state = reduceTurn(
                 (await this.turnRuntime.getTurn(turnId)).events,

apps/x/packages/core/src/application/assistant/skills/web-search/skill.ts

@@ -1,52 +0,0 @@
-export const skill = String.raw`
-# Web Search Skill
-
-You have access to two search tools for finding information on the internet. Choose the right one based on the user's intent.
-
-## Tools
-
-### web-search (Brave Search)
-Quick, general-purpose web search. Returns titles, URLs, and short descriptions.
-
-**Best for:**
-- Quick lookups for things that change ("current price of Bitcoin", "weather in SF")
-- Current events and breaking news
-- Finding a specific website or page
-- Simple questions with direct answers
-- Checking a fact or date
-
-### research-search (Exa Search)
-Deep, research-oriented search. Returns full article text, highlights, and metadata (author, published date).
-
-**Best for:**
-- Exploring a topic in depth ("what are the latest advances in CRISPR")
-- Finding articles, blog posts, papers, and quality sources
-- Discovering companies, people, or organizations
-- Research where you need rich context, not just links
-- When the user says "research", "find articles about", "look into", "deep dive"
-
-**Category filter:** Use the category parameter when the user's intent clearly maps to one: company, research paper, news, tweet, personal site, financial report, people.
-
-## How Many Searches to Do
-
-**CRITICAL: Always start with exactly ONE search call.** Pick the single best tool (\`web-search\` or \`research-search\`) and make one request. Wait for the result before deciding if more searches are needed.
-
-**NEVER call multiple search tools simultaneously.** No parallel web-search + research-search. No firing off two web-searches at once. Always sequential: one search at a time.
-
-Only make a follow-up search if:
-- The first search returned truly uninformative or irrelevant results
-- The query has clearly distinct sub-topics that the first search couldn't cover (e.g., "compare X and Y" after getting results for X only)
-- The user explicitly asks you to dig deeper
-
-One good search is almost always enough. Default to one and stop.
-
-## Choosing Between the Two
-
-If both tools are attached, prefer:
-- \`web-search\` when the user wants a quick answer or specific link
-- \`research-search\` when the user wants to learn, explore, or gather sources
-
-If only one is attached, use whichever is available.
-`;
-
-export default skill;

apps/x/packages/core/src/sessions/headless.ts

@@ -1,41 +0,0 @@
-import type { z } from "zod";
-import type { UserMessage } from "@x/shared/dist/message.js";
-import type {
-    ConversationMessage,
-    RequestedAgent,
-} from "@x/shared/dist/turns.js";
-import type { ITurnRuntime, TurnOutcome } from "../turns/api.js";
-
-// Standalone turns for non-session callers (background tasks, live notes,
-// knowledge pipelines, scheduled agents): sessionId null, automatic
-// permissions, no human. Never appears in the session index; callers keep
-// the turnId if they need history.
-export async function runHeadlessTurn(
-    turnRuntime: ITurnRuntime,
-    input: {
-        agent: z.infer<typeof RequestedAgent>;
-        context?: Array<z.infer<typeof ConversationMessage>>;
-        input: z.infer<typeof UserMessage>;
-        maxModelCalls?: number;
-        signal?: AbortSignal;
-    },
-): Promise<{ turnId: string; outcome: TurnOutcome }> {
-    const turnId = await turnRuntime.createTurn({
-        agent: input.agent,
-        sessionId: null,
-        context: input.context ?? [],
-        input: input.input,
-        config: {
-            autoPermission: true,
-            humanAvailable: false,
-            ...(input.maxModelCalls === undefined
-                ? {}
-                : { maxModelCalls: input.maxModelCalls }),
-        },
-    });
-    const execution = turnRuntime.advanceTurn(turnId, undefined, {
-        signal: input.signal,
-    });
-    const outcome = await execution.outcome;
-    return { turnId, outcome };
-}

apps/x/packages/core/src/sessions/index.ts

@@ -1,7 +1,6 @@
 export * from "./api.js";
 export * from "./bus.js";
 export * from "./fs-repo.js";
-export * from "./headless.js";
 export * from "./in-memory-session-repo.js";
 export * from "./repo.js";
 export * from "./session-index.js";

apps/x/packages/core/src/sessions/sessions.test.ts

@@ -17,7 +17,6 @@ import type {
 import { TurnInputError } from "../turns/api.js";
 import { HotStream } from "../turns/stream.js";
 import { TurnNotSettledError } from "./api.js";
-import { runHeadlessTurn } from "./headless.js";
 import { InMemorySessionRepo } from "./in-memory-session-repo.js";
 import type { ISessionRepo } from "./repo.js";
 import { SessionsImpl } from "./sessions.js";
@@ -823,26 +822,6 @@ describe("startup scan (13.6)", () => {
     });
 });
 
-describe("headless standalone turns (13.8)", () => {
-    it("runs a standalone turn with sessionId null, auto permission, no human", async () => {
-        const fake = new FakeTurnRuntime();
-        const { turnId, outcome } = await runHeadlessTurn(fake, {
-            agent: { agentId: "background-task-agent" },
-            input: user("summarize"),
-            maxModelCalls: 3,
-        });
-        expect(fake.createTurnInputs[0]).toEqual({
-            agent: { agentId: "background-task-agent" },
-            sessionId: null,
-            context: [],
-            input: user("summarize"),
-            config: { autoPermission: true, humanAvailable: false, maxModelCalls: 3 },
-        });
-        expect(outcome.status).toBe("completed");
-        expect(fake.advanceCalls).toEqual([{ turnId, input: undefined }]);
-    });
-});
-
 describe("active-skill carry-forward", () => {
     const skillTool = {
         toolId: "builtin:file-writeText",