fix(desktop): stop background session messages bleeding into the active transcript

A still-busy background session (one the user toggled away from) keeps
emitting updateSessionState() heartbeats — stream deltas, and especially
the 'session busy' prompt-rejection errors from auto-drained queued turns.
Each call invoked syncSessionStateToView() unconditionally, staging that
session's messages into the shared $messages view.

flushPendingViewState() guarded against the wrong session reaching the
view, but only one requestAnimationFrame is scheduled per frame and
pendingViewStateRef holds just the latest writer. So within a single
frame a background write could overwrite an already-pending foreground
write, and the stale background transcript (e.g. the red 'session busy'
rows) would render on top of whatever session the user switched to —
appearing to 'bleed' into every session.

Guard at the staging site: a session may only stage into the view when
it is the currently-active session. Background sessions still update
their own cache entry; they just never touch $messages. Pure render
fix, no behavior change to queuing, interrupt, or drain.

apps/desktop/src/app/session/hooks/use-session-state-cache.ts

@@ -95,6 +95,19 @@ export function useSessionStateCache({
 
   const syncSessionStateToView = useCallback(
     (sessionId: string, state: ClientSessionState) => {
+      // Only the currently-viewed session may stage into the shared `$messages`
+      // view. A background session (e.g. one still busy and emitting stream /
+      // error updates after the user toggled away) must update its own cache
+      // entry but never the view — otherwise its messages clobber the
+      // foreground transcript and appear to "bleed" into every other session.
+      // The flush below also re-checks the active id, but staging here is what
+      // prevents a background write from overwriting an already-pending
+      // foreground write within the same animation frame (only one RAF is
+      // scheduled, so the last `pendingViewStateRef` writer would otherwise win).
+      if (sessionId !== activeSessionIdRef.current) {
+        return
+      }
+
       pendingViewStateRef.current = { sessionId, state }
 
       if (viewSyncRafRef.current !== null) {