fix(studio): resync the shared SDK session after a Design-panel variable promote

Reported as "template variables are broken": binding an element's field to a
variable via the flat inspector's "◇ var" promote chip (or editing an
already-bound field's value) wrote the correct bytes to disk, but the
Variables tab kept showing the pre-edit value until the whole Studio page
was hard-reloaded.

Root cause: DesignPanelPromoteProvider deliberately opens its OWN SDK
session (`useSdkSession(projectId, selection.sourceFile ?? activeCompPath)`)
so that promoting inside a sub-composition binds the variable in the
sub-comp's own file, not the host's. For the common case — a top-level
element, same file as `activeCompPath` — this session is a SEPARATE
in-memory `Composition` instance from the shared one `VariablesPanel`
(Variables tab, Slideshow, etc.) reads. A persist through the promote
provider's session never fires the shared session's own "change" event.

Worse, the shared session's file-change listener runs
`isSelfWriteEcho(path, content)` to decide whether to reload — but
`sdkSelfWriteRegistry` is keyed by file path only, not by session instance
(its own doc comment assumes "the studio process has a single SDK session
lifecycle at a time"). It sees the promote provider's write registered
under the same path and concludes it's its own echo, permanently
suppressing the reload it actually needs.

Threaded `forceReloadSdkSession` (the same mechanism every other
server-side-write path in Studio already uses for exactly this "resync
after a write I didn't make myself" case) from App.tsx through
StudioRightPanel into DesignPanelPromoteProvider, and call it after every
successful promote/setDefault persist — unconditionally, not gated on the
promote target matching activeCompPath, since re-opening a file that
didn't change is a harmless no-op re-parse and a path-equality guard here
already produced one subtly wrong comparison (activeCompPath can be null
while the shared session still defaults to "index.html") before landing on
this simpler version. Verified live: editing a variable-bound field's
value now updates the Variables tab immediately, no reload required.

App.tsx crossed the 600-line file-size gate after threading the new prop;
extracted the tiny handleAddAssetAtPlayhead wrapper into its own
useAddAssetAtPlayhead hook (with a regression test) to bring it back under.

Full studio suite (2639 tests) green against a fresh main; typecheck/
oxlint/oxfmt clean.

packages/studio/src/hooks/useAddAssetAtPlayhead.test.ts

@@ -0,0 +1,44 @@
+// @vitest-environment happy-dom
+
+import React, { act } from "react";
+import { createRoot } from "react-dom/client";
+import { afterEach, describe, expect, it, vi } from "vitest";
+import { usePlayerStore } from "../player";
+import { useAddAssetAtPlayhead } from "./useAddAssetAtPlayhead";
+
+(globalThis as unknown as { IS_REACT_ACT_ENVIRONMENT: boolean }).IS_REACT_ACT_ENVIRONMENT = true;
+
+afterEach(() => {
+  document.body.innerHTML = "";
+});
+
+describe("useAddAssetAtPlayhead", () => {
+  it("drops the asset on track 0 at the current playhead time", () => {
+    usePlayerStore.getState().setCurrentTime(4.5);
+    const handleTimelineAssetDrop = vi.fn();
+    let addAsset: (assetPath: string) => unknown = () => undefined;
+
+    function Harness() {
+      addAsset = useAddAssetAtPlayhead(handleTimelineAssetDrop);
+      return null;
+    }
+
+    const host = document.createElement("div");
+    document.body.append(host);
+    const root = createRoot(host);
+    act(() => {
+      root.render(React.createElement(Harness));
+    });
+
+    act(() => {
+      addAsset("assets/clip.mp4");
+    });
+
+    expect(handleTimelineAssetDrop).toHaveBeenCalledWith("assets/clip.mp4", {
+      start: 4.5,
+      track: 0,
+    });
+
+    act(() => root.unmount());
+  });
+});

packages/studio/src/hooks/useAddAssetAtPlayhead.ts

@@ -0,0 +1,21 @@
+import { useCallback } from "react";
+import type { TimelineElement } from "../player";
+import { usePlayerStore } from "../player";
+
+/** Drops an asset onto track 0 at the current playhead time. */
+export function useAddAssetAtPlayhead(
+  handleTimelineAssetDrop: (
+    assetPath: string,
+    placement: Pick<TimelineElement, "start" | "track">,
+    durationOverride?: number,
+  ) => unknown,
+) {
+  return useCallback(
+    (assetPath: string) =>
+      handleTimelineAssetDrop(assetPath, {
+        start: usePlayerStore.getState().currentTime,
+        track: 0,
+      }),
+    [handleTimelineAssetDrop],
+  );
+}