fix(app): source composer cwd from agent state, not draft hook

The GitHub picker showed "No results found." for any running agent after
the first message was sent. useAgentInputDraft owned a local cwd state
that clear("sent") wiped to "", so the composer read cwd: "" even though
the agent's real cwd was correct on the wire.

Drop cwd ownership from the hook. Composer takes cwd as a prop sourced
by the parent — agentState.cwd for running agents, composerState.workingDir
for drafts, sourceDirectory for setup flows. The hook now persists only
{text, attachments}. Legacy persisted drafts with a cwd field still
hydrate; tagged COMPAT(draft-cwd) for removal after 2026-11-09.

Also moves attachment pills back inside the composer's bordered surface
via a new attachmentSlot prop on MessageInput, and shrinks pill height
from 48 to 32 — the subagents-track tuck previously had attachments
floating between it and the input.

Adds one Playwright spec asserting the draft-create-agent path submits
the workspace cwd.

packages/app/e2e/workspace-cwd.spec.ts

@@ -1,5 +1,5 @@
-import { test } from "./fixtures";
-import { clickNewTerminal } from "./helpers/launcher";
+import { expect, type Page, test } from "./fixtures";
+import { clickNewChat, clickNewTerminal } from "./helpers/launcher";
 import {
   expectTerminalSurfaceVisible,
   focusTerminalSurface,
@@ -8,6 +8,55 @@ import {
   waitForTerminalContent,
 } from "./helpers/terminal-perf";
 
+async function installCreateAgentRequestRecorder(page: Page): Promise<void> {
+  await page.addInitScript(() => {
+    const requests: unknown[] = [];
+    (
+      window as typeof window & {
+        __paseoE2eCreateAgentRequests?: unknown[];
+      }
+    ).__paseoE2eCreateAgentRequests = requests;
+    const originalSend = WebSocket.prototype.send;
+    WebSocket.prototype.send = function (data) {
+      if (typeof data === "string") {
+        try {
+          const parsed = JSON.parse(data) as {
+            type?: unknown;
+            message?: { type?: unknown };
+          };
+          if (parsed.type === "session" && parsed.message?.type === "create_agent_request") {
+            requests.push(parsed.message);
+          }
+        } catch {
+          // Ignore non-JSON frames.
+        }
+      }
+      return originalSend.call(this, data);
+    };
+  });
+}
+
+async function getRecordedCreateAgentCwd(page: Page, message: string): Promise<string | null> {
+  return page.evaluate((expectedMessage) => {
+    const requests =
+      (
+        window as typeof window & {
+          __paseoE2eCreateAgentRequests?: Array<{
+            initialPrompt?: string;
+            config?: { cwd?: string };
+          }>;
+        }
+      ).__paseoE2eCreateAgentRequests ?? [];
+
+    for (const request of requests) {
+      if (request.initialPrompt === expectedMessage) {
+        return request.config?.cwd ?? null;
+      }
+    }
+    return null;
+  }, message);
+}
+
 test.describe("Workspace cwd correctness", () => {
   test("main checkout workspace opens terminals in the project root", async ({
     page,
@@ -26,6 +75,32 @@ test.describe("Workspace cwd correctness", () => {
     await waitForTerminalContent(page, (text) => text.includes(workspace.repoPath), 10_000);
   });
 
+  test("draft tab creates an agent in the workspace cwd", async ({ page, withWorkspace }) => {
+    test.setTimeout(60_000);
+
+    await installCreateAgentRequestRecorder(page);
+    const workspace = await withWorkspace({ prefix: "workspace-cwd-draft-agent-" });
+    await workspace.navigateTo();
+
+    await clickNewChat(page);
+    const composer = page.getByRole("textbox", { name: "Message agent..." }).first();
+    const message = `cwd draft create ${Date.now()}`;
+    await expect(composer).toBeEditable({ timeout: 15_000 });
+    await composer.fill(message);
+    await composer.press("Enter");
+    await expect(page.getByText(message, { exact: true }).first()).toBeVisible({
+      timeout: 30_000,
+    });
+
+    await expect(page.locator('[data-testid^="workspace-tab-agent_"]').first()).toBeVisible({
+      timeout: 30_000,
+    });
+
+    await expect
+      .poll(async () => getRecordedCreateAgentCwd(page, message), { timeout: 30_000 })
+      .toBe(workspace.repoPath);
+  });
+
   test("worktree workspace opens terminals in the worktree directory", async ({
     page,
     withWorkspace,