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/components/StudioRightPanel.tsx

@@ -51,6 +51,19 @@ export interface StudioRightPanelProps {
   /** Dependencies for the Slideshow persist callback, threaded from App.tsx. */
   sdkSession: Composition | null;
   publishSdkSession: NonNullable<UseSlideshowPersistParams["publishSdkSession"]>;
+  /**
+   * Forces THIS `sdkSession` to re-open from disk. DesignPanelPromoteProvider
+   * opens its own separate SDK session scoped to the selected element's own
+   * file (needed so promoting inside a sub-composition binds a variable there,
+   * not on the host) — for a top-level selection that's the SAME file this
+   * session already has open, so a write through that other session leaves
+   * this one holding stale in-memory content. The self-write-echo registry
+   * that normally suppresses redundant reloads is keyed by file path only, not
+   * by session instance, so it wrongly treats the sibling session's write as
+   * "our own echo" and never reloads on its own — this must be called
+   * explicitly after such a write.
+   */
+  forceReloadSdkSession?: () => void;
   reloadPreview: () => void;
   domEditSaveTimestampRef: MutableRefObject<number>;
   recordEdit: (entry: {
@@ -71,6 +84,7 @@ export function StudioRightPanel({
   onToggleRecording,
   sdkSession,
   publishSdkSession,
+  forceReloadSdkSession,
   reloadPreview,
   domEditSaveTimestampRef,
   recordEdit,
@@ -336,6 +350,7 @@ export function StudioRightPanel({
       recordEdit={recordEdit}
       reloadPreview={reloadPreview}
       domEditSaveTimestampRef={domEditSaveTimestampRef}
+      forceReloadSharedSdkSession={forceReloadSdkSession}
     >
       <PropertyPanel
         projectId={projectId}